Well, I don’t think people in any meaningful numbers would want to migrate to a colder climate unless they already had begun wearing clothes for warmth.
Several things can be true. Also note alternative adaptation. Europeans grew facial hair for protection from the cold, whild northeast Asia you find flatter noses which I presume also is protecton against frostbite on the tip of the nose.
Unfortunately, unlike stone tools, it’s hard to find exactly when early man started making use of animal pelts of even beds of leaves as nightime cover.
There are some indications. The simultaneous evolution of human body lice and humans may provide an answer.
Molecular evolution of Pediculus humanus and the origin of clothing
Is there really any evidence that early hominids, before Homo Sapiens or Neandertals, had hairy bodies? Or have we been assuming that the first people out of the trees, out of Africa, were just smarter chimpanzee cousins? Are we really sure that Homo Habilis wasn’t already naked?
Maybe that assumtion is incorrect and that our early species of hominid weren’t as hairy as we think.
The divergence of human lice into two separate species, head and body lice, goes back a long, long way. Longer than tool making, and probably longer than clothes. The hairy ape who lost their hair so they could run down and chase game is probably a million years out of date.
Is there any evidence for hairy bodied ancestors?