I'm probably crazy, but on my old bike, I rode with lightly treaded "commuter tires" even in an inch of snow.
The tricky bit for me was keeping speed down through turns. One wrong input and you wipe out turning. That said, even when everything was shut down and state of emergency, I could still do a lap on my street till road use was allowed in the late morning this past winter.
Biggest constant problem is how narrow roads can get with half-butted plowing that didn't even clear to the outer lane marker white line. I didn't ride in lane with old bike, so suddenly being forced into traffic on those days was....interesting. With new bike I think I will invest in some studded tires that clear the fenders & brakes.
- Andy