Expanding on your excellent answer, the real difference between studded and unstudded winter tires isn't just how the perform on ice, but on ice as the temperature approaches freezing. At very cold temps, the unstudded actually have an advantage. The ice is too hard for the studs to penetrate, and the softer rubber of the studless stops a bit shorter.
But as the temperature warms to freezing and the ice gets softer, the studs really come into their own. The studded tires have an even shorter stopping distance than they did at 0F/-20C, but the unstudded start sliding and almost never stop. In the worst case, the stopping distance can be almost 3x longer than the studded!
Here's an accurate (although biased) summary of a Russian study about this: http://www.skstuds.ca/2015/10/04/the-studless-tire-deception.... Clicking through to the Google translate of the original gives even more info.
I live in Vermont, and use studless winter tires for the winter months. On snow they are great. On cold clear roads, they are much better than All Seasons. But if you hit black ice on a thawing road, you need to know that they will not stop you the way a studded tire would.
