Four wheel drive is “dumb” in that it simply sends equal power to all four wheels. But if one wheel loses traction, then a quarter of your available power is wasted as that wheel just spins (this is a gross oversimplification). All wheel drive, by contrast, operates like four wheel drive but uses a fancy differential instead of a transfer case. If the system detects that one wheel loses traction, it can selectively direct power to the other wheels instead of wasting it. It can also lock the center differential so that it behaves like a transfer case if you want. I don’t know the specifics of the park service’s rules, but an all wheel drive vehicle should do just as well if not better than a four wheel drive one.