Modern performance tires' treads aren't made for snow - too much rubber surface and not enough open space between the tread blocks.
An S-rated "all-season" tire will work much better, but probably won't come in sizes bigger than 16 inches for a while. My '64 with 295-50x15 BFG Radial T/A's is not bad in light snow if you use a light throttle foot.
For that matter, you can lose traction and spin around on dry pavement with too heavy a foot!