We've had long discussions about AWD several times before.
It doesn't help with braking or cornering, so it's really only useful for acceleration.
Tire choice or chains make all the difference in the world.
If you run out of ground clearance, you're probably going to get stuck.
I'd probably attempt the trek because adventure is my personality. A shovel is a good idea. I prefer a square-point, or a snow shovel to the Army one.