There are tires with spikes, which actually retract when depending on the tire pressure. It's quite ingenious. Also more practical options with just deeper profiles.
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.
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.
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.