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Here's a photo I took when I first got my C5. When I was done, I couldn't drive the C5 back into the garage. It just sat there and spun a wheel. The C2 (on badly worn old radials) drove off fine. The conclusion I came to was that the stock Goodyear runflats were useless on snow (and probably on cold roads).
You could easily end up wrecking your car if it doesn't have (at least) all season tires.
By the way I didn't see your thread until after you said you were going to leave. Next time don't take the Vette if are going to use chains. The owner's manual says not to use chains. The problem isn't just clearance to body panels. There are other things that can be damaged and make the car undriveable.
I run 245/45-17 on all corners with no problems getting in one night with the cables. I bought the chains for insurance as it's better than leaving it parked somewhere when you caught out. I don't run any extra weight in the rear so it's a little slow from a stop but once 40 MPH I can pull on most 4WD trucks!