Cars with the right Blizzak tires won't do that. Those WS-70's are like Snow Spiderman Sticky Feet for your car on snow and ice. You have to drive them to believe them. I've had a couple of pairs (along with a couple of other brands of winter tire). The Blizzaks don't have quite the tread life or performance of some other winter tires, but they are by far the stickiest you can buy, and that's what we'll get for the Lexus and the Prius in the next month or so.
People are utterly clueless about two aspects of car ownership: mpg's and winter tires. Anyone who says to me 'I have 'all season' tires' is telegraphing their cluelessness to the world. There is NO such thing as 'All Season' in tires. There are winter tires, and there are non-winter tires. Living up here, you want winter tires on your car if it's not a 4 x 4. Four of them.