I've climbed snow-covered mountain roads (more like trails really. unpaved roads in a state park) in upstate New York in a Honda Accord plenty of times (friend has a rather remote cabin...).
Some people do legitimately have a need for larger vehicles. The farmer I use to work for had 4 or 5 F-150s to be used on the farms (no way you are getting a regular car in and out of some of those waterlogged fields). Those were farm equipment, not something you use to drop off the kids at school. People who need vehicles like that to go grocery shopping are an extreme minority.
No, it isn't. There is absolutely no need to have a truck-based, tall monster of a vehicle in even the most serious of winter conditions in the United States. 1: places will close of road conditions are that bad. 2: a front wheel drive with good snow tires is plenty good. 3: if you're that scared of driving in the snow, a subaru impreza with snow tires is small and does quite well in the most extreme stuff.
Although I replied earlier that I've driven a small sports car through most of the last three or so winters, what you said is not always correct. There are many times that the snow is simply too deep for cars, even that Impreza. When you're high centered on snow, you're not going anywhere.
And I have never seen any of the roads around here closed, even when impassable by anything short of a snowmobile or a tractor.
3. That path is perfectly clear. Try driving a car with 4" of clearance through 8" of snow. It can be done with very good snow tires, but not nearly as quickly as a vehicle with more clearance.
People in wintery climates who want SUVs want them because the roads are frequently uncleared, or because they need to travel at night during a blizzard when the snow is piling high. If snow and ice removal operated 24/7, I agree that a smaller car would be just fine.
I drive my 350Z (2 door sports car) through most Minnesota winters and I live way out in the country on a dirt road. Have an SUV and a big pickup; most of the time they're not needed.