I helped an AWD SUV/crossover thing ten feet off the road a couple weeks ago. It was in very deep fluffy/dry snow, half on its side, sitting its weight on the snow rather than the tires. Only one wheel actually turned (front left). The AWD/TC system was literally out of its depth. 4WD, potentially with locking diffs, would not have had that problem. Once we pulled it enough to get some weight on the wheels, the AWD system kicked in and helped drive it back onto the road.

The guy had what he thought were snow tires (snowflake mountain symbol) but looking at the treads myself I didn't see the small grooves that imho are typical of proper snow tires. They looked like all seasons perhaps with some extra silicon to qualify for the badge.

Is my opinion from living in Michigan i.e. AWD is always a step up but rarely better than having the right tires. It depends a bit on the conditions too - are you looking out the window and wondering if your car will get stuck/make it up an incline or are you looking out the window wondering if your car is going to slide into a into a ditch/the car in front of you or is it an equal mix? AWD adds the most value when there was a heavy snow, unplowed roads, and relatively low traffic since. In any other case it’s really not all that helpful, except maybe a slippery uphill intersection but even then good tires help there and the inverse situation whereas AWD only helps in the one direction.