When we go into the next ice age the Inuit (Eskimos ) and the (Paleo-Siberian), Yeniseian, Uralic, and Altaic will become the new best-adapted people for the new world. No doubt the rest of our descendants will try to handle it with technology but in the end, those best able to be comfortable and survive with the least amount of technology are going to slowly populate the world to replace those that were too poor to live in a climate-controlled place.
It will be much as it is now. the populations of the wealthy nations would all be falling if not for the immigration from less successful places. The Japanese have an intense dislike for Korean workers BUT without them, they couldn't keep their factories running. We in the US are much the same. The Hispanic immigrants legal or not so legal are the people that feed us and build our homes. There is no way that you could get an American on welfare to work in the fields, or on a construction crew, or in the huge slaughterhouses that KC is full of to feed us.
In the end, it is always going to be the poor that will populate the earth while the rich and pampered members of the wealthy cultures will slowly fade out. The poor will adapt. They don't have a choice. The top of the population as far as wealth will resist change and that just doesn't work.