This is my first year riding a cyclocross bike in the winter. I'm riding a crosscheck with 40mm Nokian studded tires. So far, I love it.
I still ride the mountain bike when the snow or slush gets deep, but here in Anchorage, that's limited to a few days after a snowfall. By then, the plows have been out, the paths are clear, and the snow is packed down.
The crosscheck is no where near as stable as the mountain bike, but it's stable enough on a firm surface, and it's a heck of a lot faster.