I also migrated from a lowered Audi Quattro (B7 Avant), so this might be relevant: I’m not sure what era Quattro you had, but mine was from the Torsen era, which is arguably the best system ever put in a passenger car. The AWD Tesla system is good, but not quite that good. It’s not full-time AWD, but rather reactive and dynamic based on detected traction needs. It’s also not 50/50. With snow tires and appropriate driving technique, it will perform better than most AWD systems, but it’s just a degree below Torsen Quattro. It’s a shame because Tesla could probably match it if they gave us a full-time 50/50 snow mode for the non-P models.
As for your other questions, snow driving/handling is a separate issue from how the car fares in “cold” weather (battery performance, heater impacts, frozen door handles, wipers can’t be raised off glass, etc). It’s never really very “cold” here in the PNW, but we do get a lot of snow.