I won't ride on any roads once it's snowed and until its melted. I've seen too many cars sliding completely out of control. Even safe drivers loose control sometimes. It's not worth it for me. It's also a lot more of a pain for drivers to deal with slow bicycle riders in snowy/slushy conditions than dry.

Fortunately I can get many places (cafe's, grocery, hardware store, wine store, etc.) on paths and our city does a pretty good job of keeping them below a couple of inches or so between about 5a and 11p so snow is usually not a problem, but if they can't keep up and the paths had 4" I'd likely not ride unless it was really lite powder. I do have Schwalbe Marathon Winter's on which help with ice and hard pack. Depending on wind I'll also use alternatives if it's below about 0 to 10f.