Here are my experiences.
Drove front-wheel drive cars equipped with all-seasons from roughly 1985-2000.
Audi Quattro (i.e., four-wheel drive) A4, OEM and ordinary replacement all-seasons, 2000-2010.
Various other cars, all front-wheel drive, 2010-2013.
My experience was that the Quattro was excellent in the snow -- again, with only regular all-seasons.
2013 Tesla Model S P85+, 2013-2016. I ran with:
+ summer - OEM Michelin Pilot Sport 2s, staggered 21" performance tires, OEM Tesla 21" wheels
+ And replacement PS2s when I wore out the originals
+ winter - 19" Nokiian Hakkapollitta R2s + 19" Rial wheels
I experienced great handling summer and winter. Note that the '13 P85+ is rear-wheel drive only. I also enjoy winter driving on snow and ice, unlike many other people. I had to turn off traction control to get the car to slide around easily. Otherwise, with traction control on and careful driving, the car remained planted on the road. I frequently passed other vehicles that had slid off the road or otherwise failed to meet winter conditions. I'd say the car handled as well as my previous Audi Quattro A4 EXCEPT (1) the Tesla is much heavier, so the laws of physics dictate that a responsible driver will take that weight into account and (2) the Tesla is also significantly larger, same comment applies.
I also had an opportunity to drive the P85+ one December for about a week on summer tires; another P85 around the same time for a week using all-seasons and my own P85+ again with my winter tires. I was blown away by the poor -- I would argue dangerous -- handling of the summer tires in the cold of a Massachusetts December. (Wasn't even snowy or icy.) The all-seasons did better, but the winter tires were by far the best.
As a result of that experience, I also purchased and ran winter tires for my Prius, which markedly improved its handling.
All of the above was in Massachusetts, across some reasonably snowy winters. Also, I will note that I took repeated advantage of the Tesla air suspension to go over the top of many a patch of snow.
My current Tesla is a December, 2016 P100DL... running on summer tires! There's no good excuse for my laziness on the tires. I can hear them squealing in the morning when they are at their coldest and I'm maneuvering out of the driveway. Cold rubber is NOT the best thing AT ALL for vehicle handling. I do NOT recommend doing as I have done. It's just that, having relatively recently moved here to Maryland (where I got the new car), I haven't yet found a specialty tire shop to work with that will store my off-season tires and wheels. So I have stacks of tires and wheels sitting in my garage, waiting for me to be more responsible.
What I would ask you to think about is that the winter tires offer superior handling *in the cold* and not just in the snow and ice. The Hakka R2s are amazing, but expensive, and if you don't order them in advance, you might find the supply runs out around November. You can certainly purchase cheaper but good winter tires.
If you were to stick with a common wheel size -- say, 19" -- for both summer and winter, then you can swap out the tires without swapping the wheels. But having two sets of wheels makes the swap even easier.
The tires will also last longer because you're not putting as many miles on them per year.
I never used to think much about cars, much less spend any brainpower whatsoever on tires. Who cared. Tesla has certainly changed my thinking about cars. And a closer look at the tires has taught me that this is the only place where the car connects with the road and so it matters a great deal whether the tire can handle the ambient road and weather conditions.
In your situation, even with your current car, if your area of Ohio experiences as much snow and ice as I imagine it might, I'd encourage you to "invest" in a damned good set of winter tires. A second set of wheels is a nice plus but probably not an absolute requirement. I'd do this *even on a dual-motor configuration*. You could save $5K by going rear-wheel drive only. In fact, if it came down to a choice between AWD @ $5K and great tires @ $1300, I'd go for the tires. Tesla traction control and careful driving will tame the monstrous torque of the RWD car. That said, the second place I'd spend my dollars is on the dual-motor config. There's a helluva lot to be said for handling and performance when the computer in your car can adjust power to the wheels every few milliseconds. If you need to save money, don't buy the Full Self-Driving option -- let everyone else spend the next few years getting it to work.
Skip the UHFS sound system -- I like it, but plenty of people say the base sound system is fine, or that you can get a better sound system as a third-party purchase. You can save some money on a cheaper paint job -- which will still look awesome! -- or on various interior options. A BIG way to save money is to buy a regular car instead of the Performance option. The regular car today offers the acceleration I had 3 years ago in a Performance car! Plus the regular car offers better mileage. Try to get at least a 90 kwh battery -- this is an area of disagreement, but I believe in having as much range as you can, which translates into more options when doing cross-country trips or longer periods of roaming around home before worrying about a charge.
The Tesla Model S is a revolution compared to previous sedans, compacts and other vehicles I've driven. Every morning, I have a full battery. I have visited the gas station only a few times in three years, all to purchase sundries or make use of the facilities. The handling and performance are amazing. The safety - astounding. The people and cargo capacity - surprising. You will find stories in this forum of people who have had bad experiences and people who have had fantastic experiences. Everything you read here should be taken with a grain of salt. I think of it this way: when next you purchase a car, you can buy into the tail-end of the 100-year wave of internal combustion development. It's a fully mature technology with fully mature manufacturing. Innovation hasn't ended but the revolution is now about integrating non-ICE technologies such as batteries and electric charging. Or you can buy into the front-end of a wave of absolute upheaval in personal transportation -- full electrification, re-thinking of how a car is laid out, new opportunities for automation and driver support and attendant possibilities of pleasure and pain. I think you know which choice I made.
Good luck.
Alan