Snowplows don't remove all the snow usually because it would damage the road a lot, so you are left with packed snow which is fine to ride on.
You can also use studs tires if you worry.
I ride my bike in Sweden frequently even with a lot of snow without trouble. The only thing to worry about is when spring comes and the snow melts by day and freezes at night but on the main bicycle lanes the problem is solved by salting them once the weather gets mild.
I use a regular gravel bike (so not huge tires, 38mm) without stubs tires. Never fell.
I just don't ride during snowstorms directly of course but in those cases even buses and trains can be canceled until it calms down a bit.