The New England climate that I've lived in for the bulk of my life is very close to Copenhagen's. I also love the winter and I exercise vigorously almost daily, working up a sweat out in the woods. Amazingly enough, most people during the course of human history didn't have access to fancy fabrics, yet we managed to not get "killed". Living in a city has the added advantage of having any number of heated establishments that you can step into if you're about to die.
My experience is in areas with far colder winters. And cross-country skiing for long distances through public land, with only occasional shelter. Before there were cellphones.