For snow and ice covered paved roads, go with a tall skinny "pizza cutter" tire that is well siped. The more sipes, which are cuts made in the tread surface, the better traction you will have on ice.
There is also something called a "kerf" which is not a cut but is a molded slot in the tread... which is not as good at ice traction as a true sipe is which is actually a small skinny cut in the tread... which does not damage the tread at all. In fact, siping can help tires last longer because siped tires run a tad cooler.
If you've ever noticed the bottom of a Sperry Topsider boating deck shoe, you'll notice it is covered in hundreds of sipes that are cut into its surface which improves traction on wet boat decks. Siping was actually invented by a London butcher named John Sipe who discovered cuts in his boot soles improved traction on his slick butcher shop floors.
This pic shows siping...