I would be real interested in how my state would try to regulate such a thing. You don't need a license for a lawnmower, or a snowblower, or roto tiller, all of which are walk behind, self propelled motor driven gadgets. No license for a riding lawn mower or lawn tractor. So in that sense, this is a tractor type thing. You don't really ride on it. But it has the same result as a snowmobile.
Come to think of it, why couldn't you take your lawn tractor out on the ice?