In Denmark, it's not so bad actually. While winters tend to be miserable in their dark grayness, they're rarely very cold. The risk of rain is higher, but any day throughout the year could be wet. In other words, with a bit of gearing up, especially with a shower at your destination, year-round bike commuting in Denmark is completely feasible.
Not that cycling in freezing rain doesn't objectively suck.
Of course, salted roads can give you the worst of both worlds: wet & very cold.
You have to be willing to live fairly near to work of course. For me it would probably take about the same amount of time to drive to work. It takes me about 13 minutes to cycle and rush hour traffic will slow a car down.
If I want to go longer distances I can catch a train (and take the bike for the other end) or take a bus. Occasionally hiring a car is also possible for rare occasions.
So for me using a bike is completely feasible for living in a city.