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.
How do you get the necessary traction in eg: a braking scenario on snow? Are there special tires for that?
Yes, cars in the winter can be horrible. Anytime Vienna gets a few centimeters of snow, it's pure chaos.
My dad uses a tricycle in anything more than an inch or so of snow, as a little skid on a trike is much less likely to have you coming off than on a regular bike.
But, to be honest, it never seemed worth it. They're quite good with clearing the roads of snow, and even when they are not/it stays cold, I always expected it to clear away the next day and didn't bother investing money in it.
With full snow cover, car traffic happens in a sort of extreme slow-motion. The city also sounds vastly different, with the snow softening all noise. It actually makes for a strangely surreal/serene experience. The more unusual conditions are, the more people actually start making eye contact/get in a good mood/bond over the shared experience of chaos.
Biking on a flat, packed snow-cover is actually not too bad. It's only when it becomes ice after a few days that you really have to pay attention, and the biggest danger is irregular-sized clumps of ice which cars like to put in your path.
Whilst looking out to avoid hitting cyclists a motorcyclist must also keep an eye on larger motor vehicles, of course.
The more high quality bike infrastructure there is, the less of a difference you're going to see between seasons. People are willing to tolerate sub-optimal weather on their bikes if the bike paths themselves are low-stress and well-maintained.