Well, yes it will push snow if you install a snow plow blade on it. I'm not saying it will be the correct usage for it, but--my neighbor has an older Craftsman lawn tractor, and he has installed a snow plow, tire chains, wheel weights, and whatever, on it.
the tractor is the older, dark green style, i think it is about 8-10 years old. . His tranny is not the geared type, and it does "groan" a bit, but still works. The driveways in this area are mostly level. He has a newer tractor for lawn mowing.