An early Saab also had covered front wheels, to improve economy. It was problematic though because it under certain conditions it could get packed with snow and hinder turning.
With wheel no more than a few inches wide, it won't be driving in the snow anyway.
Actually unless you're trying to drive on TOP of feet of snow, narrow is better than wide for normal driving as you cut through the snow and get to the road. Typically people will run snow tires that are 10mm narrower than their summer tires on the same rims.
Curious to see how that could possibly look, I scrounged up these pictures of a 1947 Saab prototype. Beautiful.