I have a dedicated winter bike, Trek Portland with Schwalbe Winter Marathon's 700 x 35. They worked well last year for those icy conditions. I have never tried them in heavy snow since we never really got a pile of snow in one shot, just a bunch of smaller storms. In previous years I have used mountain bikes with knobbies and they worked great in the snow, but not so great on ice.

If I lived in a snow filled climate, I would love to try a fat tire bike.