The only hindrance the Corolla has around here is related to ground clearance. As long as the tires can reach the ground well enough, it gets around pretty well all winter. It's when there is a snow fall and then the temps drop, and we get deep frozen ruts. The city plows most of the main routes, but as soon as you're into residential streets, bang, you're stuck. Luckily, the 'Rolla hasn't been stuck yet, but there is no way a Vette or car with similar clearance can get around.
I know some 911 C4 guys that equip their cars for the winter and do drive them, but have an alternative ride for those periods when the side streets are deep and difficult. Last winter, I was on one street where the HL struggled. Then I spent a bunch of time pulling everyone else to the main road.
There was one street that got wind blasted with drifts and we were about to drive onto it, and saw a 4X4 Taco high centered, so we didn't even try.