I agree, but "winter tires" are quite different from "snow tires".
Moreover, I was implicitly assuming that the stopping would be on snow, and not packed snow but, say, just snow as it fell although maybe a minute ago to several days ago.
For stopping on wet or slushy streets or just, say, 1-2 inches of snow, then, sure, "winter tires" not only help stopping but likely are better than snow tires.
But when my driveway has 8" of fresh snow, to get out I need snow tires, tire chains, or a tractor to pull me out. Then in stopping, say, from 30 MPH in such snow, nothing helps much except tire chains and there are questions about those.
Again, what is good about snow tires is that the big bumps on the tread let the tire, when it is spinning trying to drive the car, dig into the snow, kick it backwards out of the way, and let the rubber meet the road. For that, the aggressive tread, with the bumps, is essential. But the bumps work because the tire is spinning and digging, and that action won't work for stopping unless, say, going forward with, somehow, the drive wheels spinning in reverse.
The advantages of "winter tires" are how the tread cuts through water and thin layers of snow and has softer rubber with a better coefficient of friction when the rubber does meet the road.