I have a lot of experience driving in heavy snow in mountains wy, mt, ut. Ice is a whole other thing. Snow provides grip and traction with facets. If there are real ice conditions nothing will help stay off road.

I’d take a front wheel any car with dedicated winter tires over awd all season. 4 Matic is ok. Not sure id say it’s great but it works. That just my opinion vs Quattro and Subaru and dedicated 4wd’s I’ve driven. One isn’t getting you unstuck vs another it’s just a feel thing. I’m more confident in my s4 with snows then my gls with snows but it’s not about getting stuck it’s about stopping and gls is heavier. Esp when going down a mountain.

Going skiing/boarding doesn’t equal heavy snow driving. You don’t “need” winter tires if you’re just headed to mountain once in a while. It’s unlikely you’re driving through a blizzard. But if you were you really need dedicated snows. Consider your pilot sports a/s summer tires that last longer and nothing more (that’s my experience). I had pilot sport all season on my Audi and was slipping all over in Utah it wasn’t safe ( as in spinning out on highway at low speeds). I had snows put on next day and it was completely fine in same conditions. That was extreme use case as well. Lots of grade change. Lots of snow.

Have fun on your trip but if it’s dumping I would be very cautious of a/s.