I've bike commuted through the Minneapolis winters on a wide variety of tire options - 700x28 summer tires to 26x4 studded; and most everything in between.
I started on
Bontrager Connection Trail 26 x 2.0; they are fine for fair road conditions. I would leave the bike at home on days with fresh snow or ice.
An improvement that isn't studded is the
Continental Top Contact Winter; these are good on ice but not great in deeper snow.