Sunday Mass is** obligatory,** so yes, a necessity. Now, if the roads are impassible, or you have no transportation God doesn’t ask the impossible. But if it possible, yes you need to go.
Well I live in snow and ice country. What is impassible to you, is probably very passible for me!
In fact in Quebec it is very rare for a road to be impassible. It may happen in severe whiteouts or if the plows can’t keep up with the snowfall or if there’s a major accident. More usually it is due to ice, not snow. Everyone has snow tires here (mandated by law).
That said, the standard IMHO is not passible/impassible, it’s a preponderance of risk. If I had to get my wife or a child to the hospital, I would be willing to take a greater risk than for going to Mass. On the 4th Sunday of Advent I skipped Mass, which is very rare for me, because of an ice storm. The roads were still open and the main roads marginally passible, but the police were requesting people to stay home if travel wasn’t absolutely necessary as there were lots of accidents and cars in the ditch.
The other thing, if the OP can drive his dad’s car, he may not have the same level of experience as his dad, so what may be acceptable risk to his father might be a crazy risk for him.
I think we also get an automatic dispensation for missing Mass due to travel
We are not obliged to vacation in a place where Mass is easily available.
Whether in this case it is “easily accessible” or not is a matter of prudential judgment and perhaps with an element of parental obedience. If his dad says “no, you can’t take the car” or “no, I won’t drive you” if he can’t drive, then he’s off the hook. His is missing through no fault of his own.