My illiterate ancestors were beating the shit out of each other in cold northern Europe while hot-clime civilizations were inventing algebra. Can't say enough how funny the cold winter theory is.
You're so caught up on "the cold winter theory". I'm telling you that you can completely let it go. It's one (pretty good) theory to explain one selection pressure that may have contributed to some of the aggregate divergence we see across races.
Even if you started with two seperate genetically-identical groups in identical environments, over enough generations you would expect at least some variation to emerge due to random chance (accidental deaths, mate selection, DNA recombination, cultural practices, etc). That is the point I would like you to take away from this exchange.