I tried Slip Start. When I did, I got what looked like a traction control nag light. So I turned it back on. Again, this idea of asking a driver to flip back and forth between settings is unrealistic. Audi doesn't ask this of its drivers. My wife certainly isn't up to the task of flipping switches.
Turning on the defroster is expected. But beyond that, the driver needs to do concentrate on the road.
I have Nokian Hakka 9 studded on my car. Literally in a freezing rain Storm right now in Northern NH (stopped at SC). Ice build up isn't too bad, but very solid. I have not had too much experience with the car in deep snow yet, but so far feels solid.
I am very experienced in winter driving and snow tires; I also came straight from a modern Audi. The Audi was a tank no doubt. I think asking a user to flip on slip start or limit Regen is not too much to ask. Many cars have a snow mode or traction slip mode (my Audi had different levels of TC). Now that being said, a snow mode to automatically limit Regen, turn on slip, and put chill on would be great. I do agree 3 switches is a bit much and could be simplified.
I second you and other posters; 18" and Nokians (as you suggested). You bought performance snows which are moreso meant for cars that are not going through the mountains in a snow storm, but rather places with less snow coverage or short jaunts in the snow. They are better than all seasons, but not the same as true snows. But they are much better on dry cold pavement.
As for the AWD on this car vs Audi it depends on what car you speak of. The last good AWD Audi did (SUPER TOUCHY SUBJECT to Audi fans) was the last gen Quattro. It had a true center diff, but both front and rear diff were open. The newer Quattro (Quattro Ultra) is a more slip-detected system. Assuming your A7, you had the last gen Quattro (the good one), but had two open diffs (as you did not have S7 w/sport diff or RS7). In raw mechanical traction, the Tesla is at a minimum equal.
Tesla has the really cool advantage of having two wheels driven at all times; there is no way to lose all your power to open diffs.
There are so many types of AWD systems, but most AWD systems are simple and actually are 1 wheel drive in certain conditions. All the power can be lost to 1 wheel. Audi with a real center diff forced power front and rear, thus was a 2 wheel drive. If you add a limited slip diff in the back, you have 3 wheel drive. A LSD up front and you have a real 4 wheel drive. Typically only off road trucks have real 4 wheel drive (LSD front and rear, lockinglcenter diff) and some specialty rally cars (WRX STI, Focus RS, Lancer Evo). The Tesla can mimic an LSD by braking wheels that slip, but still no where as much power is delivered as with a real LSD.
Wow I did not mean to go on so long! Just at the SC and it's so cold it's only Charging at 20-40kw......
TL;DR: Tesla's AWD is on par with Quattro systems without an LSD. It is far better than most other AWD systems.