Yep, they certainly do, and if you can afford to have another set of wheels/tires, or pay to have them swapped twice a year, that's all well and good. Not to mention having a place to store the wheels/tires that aren't on the car.... Not something I am really interested in doing, thankyouverymuch.
Of course, I drive a 3/4 ton 4x4 truck, and my tires are pretty aggressive in any event. I don't have problems getting to where I need to go, even when other folks are trapped in their driveways, or in a snowdrift..... (and I keep a log chain in the truck for just such occasions......) On our van, which is AWD, I have one set of tires, also fairly aggressive, and they do just fine year round. Of course, the van won't handle the deep snow nearly as well as the truck..... but, for crappy driving conditions, it's great. (so long as the snow doesn't get too deep.) On ice, unless you have studs, or chains, doesn't matter what tires you have, you are going to have extremely limited traction.... (and both of those are illegal here.....) So, either don't drive, or go VERY slow.
I drove home from work one day, about 40 miles, after we had freezing rain. The roads were covered in black ice. Even with all-terrain tires (different truck then), and 4wd, 25 mph was too fast.... a strong wind could blow me right out of my lane, and I became a passenger with a steering wheel. Had to hold on till I hit one shoulder of the road, or the other, so I could regain control. That was a LONG ride home.....