Most all season tires, which the Michelin Primacy AS tires on GV are, have the M&S designation. For real snow and Ice, you need the 3 peak mountain. In fact, having winter tires during winter months is mandatory in a few places in Canada, and that requires the 3 peak symbol. All-season are a compromise tire. The newer category of All-Weather tire, supposedly have the 3 peak symbol making them a good choice for those that don't want to have 2 sets of tires/wheels. Also, of course, if you need this capability only once or twice a year, then having a 2nd set of dedicated winter tires is likely not worth it, and best to simply understand the tire's limitations and drive to the conditions when you do encounter snow and ice.
I live in Canada and I could not fathom driving in the winter with the stock all-season. Tires are the one point of contact between the vehicle and the road and one area I always ensure I invest in quality....safety first. I will be changing my stock 19" for winter tires, selling the Michelins, and will be purchasing a 2nd set of
aftermarket wheels (likely 22") for summer.