Copenhagen is definitely colder than Seattle, with lows below freezing all through the winter.
It's definitely harder to ride a bike in cold winter weather— but the same is true of walking and driving. One mostly needs cleared roads/paths (as drivers and pedestrians do) and warm, windproof gear (as a pedestrian and skier does). The right bike for city cycling year-round isn't a road bike designed for warm weather high-speed recreation, either.
I wear normal clothes and just add a nice wool 'Buff' scarf for face/neck coverage and good gloves for cycling around NYC in winter weather. I also use snow tires for safety, just because the city doesn't do a great job clearing snow from all the bike lanes, and the bike lane network isn't yet extensive enough that I can avoid mixing with car traffic.
And when it's really cold— even Minnesota closes schools and businesses, anyways:
https://www.mprnews.org/story/2015/01/06/school-closure-crit...
So— cycling in cold weather is perfectly possible, and, in any case, most people don't live in places where it regularly gets cold enough for cycling to be truly difficult.