They are two of the most important factors in mobility in snow.
1. Friction is directly proportional to the normal force, which is directly proportional to mass.
2. Height is massively important when driving on snow covered streets, especially those that see occasional traffic. To drive down the street you are acting as a snow plow, pushing any snow that has accumulated since the last car went through, plus or minus any difference in height between your car and theirs.
That being said, we live in a city that gets lots of snow, have 2 kids and my wife needs the ability to get to the hospital without having to wait for a plow to come past. We don't need or want an SUV. My sister with 4 kids living on a farm does.