Speculation about how long exactly a 'Winter' lasts in Westeros, partially substantiated from comments found in the books, tend to imply that the actual coming of Winter is pretty much random — i.e., Winters may be long or short, but it's safe to assume that they are at least 1-3 years long, but sometimes last a whole decade.
Now this raises a huge logistic problem. It's true that (at least in the books) people have a lot of warning that 'winter is coming' and therefore we see farmers trying to plant as much as possible, making sure they get a couple or more harvests in before winter truly sets in. So far, so good.
However, this is a fantasy/Middle Ages setting — at least on the Westeros side of the world; Braavos and the Free Cities seem to have developed a more sophisticated culture, but that's another story. This means that we ought only to have certain methods of preserving food for a long time. Out of my mind, the only way I see someone worrying about food stockage is Jon Snow, who explains that the storage of meat is done inside the Wall, which is always cold, and this would be a naturally obvious place to store food.
Nevertheless, no matter how cold the Wall might be, there is clearly a limit in how much it can store (the Wildlings soon deplete the cache held by Jon) and, of course, in its duration. In the real world we can deep-freeze meat for about a year. Let's stretch the point and believe that the Wall is able to keep it frozen for that long — after all, the Wall is certainly magical, and we know it's used as a freezer, so, ok, we can assume it's 'as good as our 21st century freezers'.
Fine. But if a Winter lasts a decade (and we know for sure that this is certainly possible), then where will be meat stored? It will spoil after a year. What will people eat then?
And of course this only applies to the Wall. Nowhere else is mentioned how food is preserved. We can therefore only presume that traditional methods for food preservation will be used. Curing, smoking, salting meat will preserve food for about a year as well, and assuming you have a whole industry able to process tons of meat for the whole population, then you could presumably survive the first year of winter without starving.
But this would assume that everybody has (relatively) cheap access to meat, which runs contrary to what a Middle Ages setting ought to be. Meat was an expensive commodity only available to the wealthy. It's not unlikely to find meat at the Wall — after all, they get it from donations and so forth — since meat would also be given to some of the soldiers, at least during the time that they would be active (in the Middle Ages, this would be little more than three months), although pillaging — which we know happens in Westeros as well — would be the best way of supplying armies with food (they would not need large baggage trains).
In other words: there is some consistency in the way food is produced in Westeros, and how the aristocracy, the peasants, and the armies are fed. Martin is clearly fond of food, since he describes it in such a minute detail. We get plenty of hints that farmers are truly able to plant a lot, and Westeros seems to be mostly very fertile (except perhaps in the far north, and, of course, in the Dorne deserts), so there is no problem in having plenty of food — even (apparently) during crushing wars, which destroy a lot of the plantations by permanent pillaging. Nevertheless, we see that most areas (and large cities) in Westeros continue to be reasonably well supplied with food. Westeros has lots of food. That makes sense during 'Summer' — in our own world, we have plenty of places where seasons are pretty much nonexistent and it is plausible to have multiple crops in a year.
So... we can safely establish that there is plenty to eat in Westeros. Now we just need to know what they eat during Winter!
One possibility, of course, is trade. In other words: because apparently only Westeros is seriously affected by Winter (Essos much less so), it's conceivable that, during Winter, Westeros would import food from the Free Cities. In fact, this could have been one of the reasons why Valyria didn't have a strong hold in Westeros before the Targaryens: it would be hard to keep everybody fed during Winter. So, let's assume that the Westerosi have solved this issue through trade — we know that trade is plenty and common among Westeros and Essos (and other further-away lands, but let's stick to those for a moment).
Ok, trade. But trade... what? Westeros seems to have only three kinds of possible exports: wine (Dorne), food (since it's so plentiful, it must be cheap during Summer), and gold (from the Lannisters). Food and wine, of course, cannot be traded during Winter — since, naturally enough, Westeros would be lacking both. They might sell a little wine at first (because wine can be bottled for much longer than a year, and it's conceivable that Dorne had acquired that knowledge from the times of Valyria — pretty much like we Europeans continued to plant wine after the fashion of the Romans, centuries after the Roman Empire collapsed), but, lacking the ability to replenish their stores, at some point — especially during very long Winters! — that supply would go out.
That means that what remains for trade is basically gold. Which, needlessly to say, is not a bad commodity to trade: it doesn't rot or spoil, it's compact, it's easy to store and to transport. And we can imagine — I have no reference, just wildly conjecturing — that possibly Valyria was not aware of the vast amount of gold under Westeros' crust, and somehow the Targaryens figured that they could survive the long Winters by mining gold and trading with the Free Cities. Of course, food prices would skyrocket during Winter, but they would be compensated after Winter, since Westeros is apparently able to produce quite a surplus of food (and wine!) during Summer. In those years, the trade routes would actually work in reverse — Westeros exporting food and getting gold in return. A good King would manage the economy so that it balances out without going bankrupt, and I think this would be manageable.
There are just two catches with this theory.
The first, of course, is that we know that the Free Cities are 'mostly wasteland' (except for the city-states themselves), and even if they are not exactly pictured as 'deserts' (like, say, the Green Sea), it's clear that whatever villages and townships that may have existed have long ago been razed to the ground by the Dothraki and their population fled to the safety of the nearest city walls. That means that all food for those cities must be imported as well. Again, this doesn't pose a problem — lots of civilizations flourished in our own Earth using ship trading to supply cities with food — but it means that, during Winter, even if Westeros is willing to pay well, and Winter does not affect the food production that already supplies the Free Cities, it would probably be too scarce anyway. In other words: during Winter, the Free Cities would hardly be able to feed themselves, never mind about selling any non-existing 'surplus' to Westeros. This clearly doesn't work.
So we need to speculate that, during Winter, there are much longer trade routes, to those continents of which we know so little, and food must be imported massively from there — to feed Westeros but also Essos. Again, we can also speculate that such extremely long trade routes only became possible thanks to an advance in naval technology only possible during a relatively peaceful period while Westeros was united under the Targaryens, and that in the times of the Valyrians such extensive trade routes would be unfeasible with existing technology (again, see the parallels between the Roman Empire and the Renaissance in our own Earth — while the Romans had an incredibly advanced naval fleet, and an astonishing amount of 'scientific' knowledge about navigation techniques and so forth, they were unable to 'escape' the Mediterranean (except for occasional ventures) — while during the Renaissance we were able to pretty much establish trade routes world-wide, in journeys that could take a year to complete, but which were highly profitable, to pay off the huge investments made in naval technology of the time — which was not cheap, and navigation knowledge was scarce, mostly a State secret, but... it still managed to give us extensively long trade routes).
This launches us into the second catch: if the above is true, then Westeros would be a major naval superpower. But we know this is not the case. It's true that each of the kingdoms do, indeed, possess relatively good fleets (some naturally in larger number than others) and that the merchant fleets are adequate for trade overseas with the Free Cities (at least those closer to Westeros...). But it seems that in terms of technology, clearly Braavos is the technological naval superpower of the age (like the Venetians shortly before Renaissance in our own world). And it makes sense, too: after all, as said, Braavos is a trading nation (and a financial one as well) and must import all its food as well (except for fish, of course), so it means tackling the issue of handling very long overseas trade routes. Braavos is also sufficiently to the north to feel the adverse issues of Winter (even if not at the same intensity as Westeros) and that might have pushed them to develop a more advanced naval technology than, say, other Free Cities.
Because Braavos — and not any city in Westeros — leads naval technology, we have therefore to assume that Westeros is not yet at the stage of being able to do long oversea journeys (or they would have quickly matched Braavos in technology, and Braavos would not be so important — naval-wise — as Martin makes us believe they are). This means they have to establish complex trading routes with lots of intermediaries, i.e. assuming that Free City 1 trades food with Free City 2, and so forth, until the most remote corners of the planet, while Westeros only bothers to trade with Free City 1. This kind of arrangement, again, is also very plausible: during the Renaissance, the Ottomans managed to connect the rich cities of Europe with the wealth-producing cities of the far East that way, and explored those trade routes commercially with huge success — until the Portuguese tricked them out... by navigating around Africa and competing with alternate trade routes... but that's another story: in Martin's world, it is conceivable that most trade happens in (relatively) short hops between the Free Cities in Essos and even with the other continents, while presumably Braavos has a better, more advanced naval technology, and might be able to do very long stretches of oversea voyages — meaning that they can cut the intermediaries, go directly to the source, buy much cheaper and get a much larger margin of profits, which would also explain very neatly their immense wealth.
The second catch is not only the necessity of developing naval technology to reach the furthest shores of Martin's planet; not even to mention that in our own history we rarely had such massive amounts of food being pushed across the oceans to feed so many people (it's a logistical nightmare); no, the problem is that during Winter, we know that the ocean — at least around Westeros and the western coast of Essos — becomes pretty much impossible to navigate, or at least so dangerous that it's not worth the cost (both in ships and human lives).
So, while this elegant theory of long supply chains of massive amounts of food over the oceans all around the four (or more) continents is a very neat, romantic idea — one that would explain Braavos wealth, but also the wealth of the other Free Cities, namely those that are huge ports and rely exclusively on food being supplied overseas — but, alas, it fails because Westeros is not reachable by sea during the Winter. One might conjecture that the seas further south, around Dorne, might be navigable during Winter, but then we have another problem: suppose that we do, indeed, use Dorne's ports to receive all the food to distribute around Westeros. What next? Take a look at the maps. Dorne is 'mostly desert'. Its major cities are near the sea or the vast rivers crossing the desert. So, yes, we might be able to supply Dorne by sea; but there are no roads to the North. Well, there are a few. But they don't lead to any seaport! (at least not to any mentioned in the maps)
Even so, picture the following scenario: galleys coming in to Dorne's seaports, vastly loaded with food (and we are talking mostly about preserved meat, of course; what else would survive long journeys across the oceans?). Picture the food for millions and millions of people. Now this food needs to be hauled over land routes, because all ports above a certain latitude will not be reachable during Winter. Imagine thousands upon thousands of ox carts and their drivers, crammed full with food, driving northwards across all roads... after crossing Dorne's deserts... and, as they drive further north, they will be subject to the harshness of Winter. And this needs to be done every day, for a whole decade, assuming a very long winter.
Does it seem practical to you? Or even feasible? Well, I could barely imagine that the Targaryens, especially if they had free access to all the Lannister gold, could conceivable organise such a vast and complex logistics operation... but we must forget that even Valyria with all its amazing, superior technology (or magic) were unable to do so.
So what is the secret of Westeros? What do they eat during the very long winters — and how do they manage to survive the Winter?
Some references to the Winter's length (as well as some explanations to mild variations among the 'year' and the ability to harvest often during the same year):