I've been snow camping in the Sierras for over 30 years, and I can tell you that one of the biggest problems is to find a safe place to park your car. In a few areas, there are Sno-Park lots. That requires a daily permit.
I've parked on the shoulder of a plowed road, off the pavement, and had my car completely buried by the snow plows to the point where it took an hour to dig out.
In the national parks, typically there are a few parking lots plowed out. Still, you need to carry at least one shovel per group, plus maybe have more in the car.