That said snow tires are still spectacular and necessary in snow. I buy and use snow tires every winter season. They are invaluable. I just am saying don't drive with them on ice and expect to have any better traction.
In real ice events/situations the tire chains come out or you just stay off the road, it's that simple. No amount of perceived driver skill, AWD techno buzzwords, etc. will save you on ice--you need hardened steel cutting into the ice.
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.
Now, I love my carbide studded bicycle tires. Those definitely do work on ice. But once again, staying upright on ice involves a combination of those tires and other precautions such as slowing down.
I live in an area of Sweden that has ice and snow at least 4 months per year. Still thinking of buying studded tires for the fatbike but want to see how I'm doing with these, the rubber is nice and soft even at -20 degrees so I think I might be good enough with this solution.