Actually, the comics don't suggest that zombies can freeze to death. In fact, quite the opposite. When the group finds the walled community of Wiltshire Estates, it is extremely cold. They sweep the area, find no zombies, and settle into the houses. Overnight, the temperature rises. A layer of snow and ice on a sheet of plywood outside the gates begins to melt, and soon we see that it is in fact a sign:
You can imagine, based on Rick's reaction and the naughty word I blacked out, how Rick feels about the warning painted on the sign. He clearly realizes that the reason the group didn't find any zombies roaming around is that they were all frozen. Now everything is thawing out, including the zombies, and Rick knows that this is a very bad thing indeed. By the time he begins to warn the others, it is too late. The zombies are up and about, and people are being attacked. One person, a woman named Donna, is killed.
This answers your question - zombies are essentially unharmed by the freezing process, and remain in a sort of hibernation until the weather allows them to thaw out and become active and mobile again.
From the Walking Dead wiki page for issue #8 of the comics:
At the road, they find a house but it's burned. Rick says they have to leave. While Glenn is filling the gas tank, Dale screams and falls down in front of a frozen zombie. Dale confirms he's not bitten, and Andrea runs to Dale and hugs him, glad to see he is unharmed. The frozen zombie moves and Glenn gets scared. Rick kills the zombie. Survivors learn the zombies freeze faster than normal humans. The group come across a group of houses enclosed by a fence, titled "Wiltshire Estates". The group proceeds to clear a house which leads them to think that they may have found a permanent sanctuary. They end up spending the night inside the cleared house. What they don’t notice is that a snow covered sign that reads “ALL DEAD DO NOT ENTER.”
This is also consistent with the holy bibles of zombie media, Max Brooks' World War Z and The Zombie Survival Guide. Because zombies aren't actually alive, they suffer no ill effects from extreme cold. Extreme heat isn't an issue either, unless it is so extreme that the zombies burst into flames. The zombie dichotomy is at work here: they are simultaneously very easy to kill and very difficult to kill. That is to say, if you know what you are doing, you can kill them without much difficulty, but they don't die very easily when left to their own devices.
The most "scientific" explanation for this is to be found in Max Brooks' books, as I mentioned above. The reason people die from hypothermia is because their body temperature drops below safe levels. Zombies, on the other hand, have no internal heat regulation system, and their bodies are roughly the same temperature as the air around them. When a person develops extreme hypothermia, the brain begins to shut down essential functions, like your heartbeat, breathing, blood pressure and circulation, etc. A zombie doesn't have to worry about any of these problems, because it is dead. It has no heartbeat, it doesn't breathe, its blood just sits in its veins and arteries rotting away, and its body temperature reflects the ambient conditions around it.
Whereas the human brain is a complex array of neurons, axions, synapses, and electro-chemical signals, all of which work in tandem with each other, and are powered by the digestion of caloric materials, the zombie brain is very different. It is largely dead tissue, slowly decomposing inside the skull, and only the brain stem is partially active.
However, even this limited activity has nothing to do with digestion or the natural electro-chemical signals present in a normal brain - it is merely the result of a virus (Note: in The Walking Dead comics, and to a lesser extent on the show, we don't know exactly what the infectious agent is - virus, parasite, fungus, etc, so it would be best to think of it as a pathogen, but for the sake of convenience, I will refer to it as a virus - as it happens, in World War Z, the infectious agent is indeed a virus, which is called "Solanum").
The virus reactivates the basic sensory and motor functions of the body. It doesn't rely on the body's natural functions of resources, and it exists only in order to spread itself to new host organisms.
The virus only activates the parts of the brain necessary for making the body detect prey, follow it, and bite it. The parts of the brain used for all other purposes are left unchanged and inactive. Even the functions we consider vital to our survival- circulation, respiration, blood filtration and oxygenation, etc, are totally irrelevant to the purposes of the virus and the zombie it creates.
And viruses are nothing if not resilient and virtually indestructible. They can survive extreme heat and cold, arid conditions, humidity, and so on, and can lie dormant for surprisingly long periods of time without dying. So when the zombie freezes, the virus basically goes to sleep and waits for spring to arrive. The zombie's muscle tissue might suffer a bit of damage from freeze/thaw cycles, but not enough to kill it.
Out of universe, there are actually a number of animals that can freeze solid for extended periods of time, then thaw out and go on doing whatever it is that they do, none the worse for wear. Perhaps the most famous of these is a species of wood frog indigenous to the northeastern U.S., which begins to produce a natural form of antifreeze (glycol, if I'm not mistaken) when temperatures drop. This prevents crystals from growing large enough to puncture cell walls, which would cause irreparable damage to the muscle tissue. When spring comes, they thaw out and hop away unharmed.
And it is worth mentioning that we're talking about mobile, cannibalistic corpses. If you are willing to accept the premise that such creatures can even exist, it probably makes sense to just accept that they don't freeze to death.