Mine now has 40K miles and I don't have ANY problems people are having. No treadwear issues or any transmission or electrical problem etc. Only issue I have is somehow idiots keep on scratching my car even when I park far away from others.
I have had many sports cars and mainly live in the Northeast. In the winter everyone I know of has a secondary vehicle. Very low clearance sports cars are not snow plows, slush filled hidden potholes are another concern as well as road salts and lack of traction. Go in a deep filled over pothole and see what I mean.
I put mine away in a garage (not a car cover that scratches paint and traps moisture) and drive even an inexpensive driver for the winter months. I had a 280ZX 2 + 2 long ago, and many other make roadsters since. I always pull them out every 3 weeks from the garage on clear days only to keep the engine seals from drying out and to prevent flat spotting of the tires, put trays of charcoal briquets in the trunk and floor of the car, kept the doors and trunk cracked to save the weatherstrips. I also do not use silicone protectorants ever.
Pick up a cheap second vehicle for the winter months. I have found being in South Florida part of the year, other weather related considerations. A convertible lasts about 4 years with the intense sun and daily brief tropical rains, perhaps longer if you have a car port. The intense heat and sun tends to warp tops and cause leaks. You also need A/C, and tint is advisable. No matter where you live, sports cars have limitations and can last if you divide the wear on another vehicle. Switching tires is not a solution in my opinion, but switching vehicles is.
If you do get caught out in the wet or bad weather, slow down is the best bet and use traction control if you have it. I almost hit the wall of my house once just exiting my driveway, another reason not to drive a powerful sports car on slick surfaces. A great second vehicle is a Jeep that you can still remove the top, have more room and drive in the snow too.
I agree about having a second vehicle. But in winter months where there isn't a lot of snow fall just really really cold. There is no reason not to continue having fun with a Nissan 370Z. Just use winter tires and tire cables/chains if need be. There is no reason why you can't enjoy your Nissan 370Z in Minnesota when it's less than -30 degrees Fahrenheit outside but clear sky's and dry roads. Once the snow starts falling, that would be the time to switch over to my 1982 Mercedes-Benz 300SD turbo diesel with snow tires and tire chains if need be. It's high torque, low horsepower, high curb weight, and low center of gravity make it ideal for North American winters on both surface roads and limited access roads that are salted and/or plowed. Just put lead weights in the trunk if need be. The car is old anyway so it wouldn't matter if it rusted.