It makes sense to me that humanity started in Africa and eventually settled in Mesopotamia, and then migrations started east and west into Asia and Europe. Ancient civilizations in China and the Mediterranean (Egypt, Greece, Rome) flourished in temperate, often sub-tropical climates where .
But after they lost power, why didn't other people move into those areas? Countries like England and Russia have brutal winters and much of Europe gets bitterly cold. Even countries like France are beautiful in the south, but Paris is in the northern part of the country.
Why didn't countries like this move or establish their capitals in more hospitable locations?
I would just like to point out that you can't possibly call English winter 'brutal', especially with regard to the Russian one.
The limiting factor to supporting a "modern" society - a relatively high population density, large urban areas - is agriculture. As long as you can grow crops such as wheat, rye, barley and others, it doesn't really matter how cold the winters are. In that sense, having summers that are warm enough and long enough is more important than having mild winters. So a cold climate isn't necessarily inhospitable especially since people have lived and created complex societies in places like northern Europe and Russia for many centuries.
Your question seems to be more focused on preference rather than habitability (in other words, "sure you can live in a cold climate, but why would you want to"). This seems likes a first world problem. For the vast majority of people in that past, choosing a place to live based on weather preferences was a luxury they couldn't afford. They had far more pressing concerns. Secondly, as I mentioned these societies were sedentary and agriculture based. Unlike for the nomadic societies, it was very difficult to just pick up and move. Lastly, warmer climates aren't necessarily better anyway. Maybe the summers are very hot and oppressive (remember that in the past, it was very easy to keep a house warm than to cool it down). Maybe the rainfall pattern is unpredictable and droughts are frequent. Maybe the soils are unsuitable for agriculture. In short, cold weather was not a big enough problem to solve, and attempting to move to warmer places would have created much bigger problems.