I first checked this out from a public library sometime in the 1980s. I believe it was written as a "juvenile" SF story . . . more-or-less what gets called "Young Adult" nowadays. English language, hardback edition, and I think the cover art had at least two guys in parkas (i.e. all bundled up for arctic conditions) trudging across a white field (snow/ice) with a dark blue sky above them. Someone may have been pulling another guy, and/or some supplies, on some sort of toboggan.
Here's what I remember about the plot:
The world is in the grip of a particularly bad ice age. For instance, the main viewpoint character is a teenager living in the underground warrens beneath what used to be New York City. His native culture still has books and higher education, and some sort of power source to keep things reasonably warm in their underground settlement. But the population is numbered in mere thousands (not even tens of thousands), rather than the millions of people who inhabited NYC in the 20th Century.
For reasons which escape me, it is deemed important to send a small expedition a very long distance to do something-or-other at another outpost of civilization. (I am thinking "a similar underground town in England," but that may not be accurate.) The point is that the trek must be made "overland" (or at least "over-ice") because sailing from NYC to the destination simply is not possible. In other words, the North Atlantic (I think) is now covered with a very thick, solid ice cap (presumably an extension of the polar ice cap that's centered around the North Pole in modern times). Either the people of NYC no longer have long-distance air travel capability, or they are unwilling to risk it on such a long trip. (I suspect they don't have it, but it's been a long time.)
I don't remember how many characters are part of the initial expedition, but it includes our teenage protagonist, along with at least one "trained scientist," an older man who is probably called "Doctor (Surname)." I don't think the "Doctor" was an M.D., but I don't remember just what the heck his specialty was.
One scene I remember fairly well is when the expedition from NYC bumps into a group who apparently live much like old-fashioned Eskimos -- wandering around on the snow and ice, hunting for food. (I don't remember what type of food.) The chieftain is a rough sort of fellow, but he's willing to talk to these strangers instead of just trying to kill or enslave them, for instance. What I remember best is when the Doctor is trying to explain about New York City (possibly called something else, such as an abbreviation of that name, or of "Manhattan") and talks about the population that lives underground in one place. He says something like "we have over four thousand people" (or some other figure in the thousands) and the chieftain initially looks blank and asks an advisor what that word "thousand" means. The advisor mutters in his ear for a moment, and then the chieftain looks at his own fingers (still in thick gloves, I suspect), and says angrily: "Ten tens of tens? There are not so many people in the whole world!" Then the Doctor tries to explain that, according to their records, many generations earlier there were at least a thousand times as many people in their city as there are now. (When things were much warmer, of course.)
I think the story ends with our hero waking up in a warm environment somewhere down in the tropics. I think the idea is that while he was unconscious after some sort of injuries, terrible exertion, and/or nasty case of exposure to extreme cold, someone had loaded him into a surviving airplane and had flown him south to someplace near the equator where it was still possible to get in a good crop of grain during the warmer part of the year. (The people of NYC had not previously been aware that such places still existed anywhere on the face of the Earth -- telecommunications were minimal or nonexistent, I suppose). I don't remember what the agenda was of these "tropical" people, but they seemed reasonably friendly.
However, the reason I kept saying "I think" in that last paragraph was that I'm by no means certain that my memory isn't splicing the final chapter of another story (perhaps with a similar "new Ice Age" theme) onto my memory of the juvenile SF novel about some people from NYC trying to cross a frozen ocean. We're talking 30 years ago or more, and my memory is far from perfect.