On my car, I use proper winter tyres as they're required by law on the continent (Europe). Proper winter tyres for snow/ice with the 3PMSF symbol. These are not common used / mandatory in the US.

In Sweden/Denmark I just used the standard bicycle and tyres and the cycle lanes were clear. In Germany, unless there was shear ice (as in an ice storm), I rode standrad MTB tyres as the paths were maintained.

In UK, if there's now/ice. I stay and the Brits can't deal with it and it's very unsafe (the university shut down due 1/2" of snow as an example).