that's wrong. why do you think alpinists use those special big shoes to walk on the snow. also, it's a known practice to let some air out of the tires when if you want to drive on snow, so that the wheels get as little into the snow.
thinner wheels are better in the snow - you get more traction as the same amount of weight (the car) is spread across a smaller area. does show you how nobody needs SUVs though!