These are a couple videos comparing the performance of all-season tires versus winter tires on Notre Dame's ice rink. Unsurprisingly to anyone with half a brain, the winter tires perform significantly better, because icy conditions are exactly what they were made for. "Don't lie, you thought winter tires were just a marketing ploy." And I still do, which is why if you really wanna be safe this winter you should buy a Zamboni.
Keep going for the videos, the second of which features vehicles with all-wheel drive. Just go buy the tires already, okay? You can store your all-season ones in my garage, but FULL DISCLOSURE: if you return to only find three, I made a new tire swing.
Thanks to Josh J, who agrees buying a tank is also a viable option.