If you're talking about riding on roads, it's not a problem. Get studded tires, ride conservatively. Black ice is not a problem.

The only time ice is a problem for me in the winter is if I have to stop. My bike gets great traction on the ice, my feet, not so much.

Heavy, wet snow is just all around miserable. I skip the bike and drive if there is more than 4 or 5 inches of unplowed stuff on the roads, if it's heavy. If it's fluff, not a big deal really.

Nokian makes the tires to get. I use to have W106s but switched to W240s because the extra rows of studs along the sides help prevent getting a tire stuck in a frozen rut, which can take you down.