Towards the end of the C5 era, I heard an interesting story from Jim Minneker, once of the Corvette development group, and now (I believe) with the Performance Division. He said that, one time in the Winter, a number of engineers set out for "Kinross" one of GM's winter testing facilities in the U.P. of Michigan. After a winter testing session, they were returning to Detroit and began driving through a sudden and heavy snowfall. They were all driving later C5s, each fitted with four Goodyear snow tires (back when GY made a mud/snow tire in those sizes). He told me that with four snow tires and ABS, ASR and Active Handling, C5s were excellent "snow cars" until the depth of new fallen snow on the road began to approach the cars' trim heights.
I don't think Goodyear sells the C5 snow tires any more, but I think Bridgestone has those sizes in its excellent "Blizzak" line. Combine an AH-equipped C5 with four snow tires and a driver with reasonable experience in winter driving and you have a pretty darn good car for freezing weather--until the snow gets deep enough to high-center the car.