I lived for over a decade in a place that was often quite cold in the winter. Like below 0°C for months, and sometimes down to -40°C for weeks. Also quite windy, so wind chill could be -50°C or below, at times.
And I didn't own a car, so bicycling was my only option. I did buy Gortex pants and jacket, though. So for riding, I wore silk underwear and sock liners, wool socks, heavy wool pants, high-top lace-up leather combat boots, a wool sweater, a neoprene face mask, and Gortex.
I wore pretty much the same kit for cross-country skiing and snowshoeing. But less for downhill skiing.
I did ski with a guy who almost froze to death, after his cotton and down got soaked.