I've gone through three Berlin winters now with going everywhere by bike. It's a one-time investment in some good clothing, mostly for hands, feet, and your head. After that, it can actually be a lot of fun to drive on fresh snow, or through the blizzard.
In my experience, cars become a lot more of a problem in winter: they're more likely not to see you because it's dark, and because rain and snow are terrible for your vision if you're behind a windshield. There are also fewer people on bikes, so they don't expect you and pay less attention. With snow, there's also a tendency for odd-shaped large pieces of ice to end up right in your path, i. e. slightly to the right of the cars' track.