Back when Mr. Burkhard taught us physics in high school, we learned about computing the size of a circle that a vehicle could negotiate based on the friction of various surfaces. So I found myself asking, "What is the deceleration that we are getting on ice with various tire types?"
The formula for computing deceleration for a particular speed down to zero over a particular distance is v^2/2x. The data that I found here for stopping with studded tires, Bridgestone Blizzaks (a superior snow tire), and all season tires from 25 mph are 106 feet, 118 feet, and 128 feet. A little arithmetic tells us that the studded tires give .135g deceleration, the Blizzaks give .121g, and the all season tires gives .118g. By comparison, most decent cars (that is to say, the kind that I like to drive) will stop on dry pavement from 60 mph in 120 feet or so, which is about .70g deceleration.
The good news is that ice is not a frictionless surface--or you would keep sliding until wind resistance slowed you down, somewhere in the next state. Even on ice, tires will eventually stop you--but not before you run into another car, or in my case, a hillside.
Ordinarily, I would make the assumption that while there differences within class (some snow tires stop better than others, some all season tires stop better than others, some studded tires stop better than others), it isn't very likely that the best tire in any of these categories is as good as the average tire. In other words, the best all season tire isn't going to decelerate as fast as the Blizzaks; the best snow tire isn't isn't going to decelerate as fast as the studded tire average. This TireRack.com report indicates, however, that in some cases, the best snow tires (such as the Bridgestone Blizzak WS60) are noticeably better than a studded tire.
What this all means is that the advantages of the average studded tire over the average snow tires is only about 12%, and over all season tires is only about 14%. (Although this TireRack.com report indicates that the best snow tires might be as much as 15% better than a studded tire for acceleration.) Why? It appears that while studs actually do punch into the ice--the ice isn't strong enough for the studs to continue to get traction. TireRack.com tested on a ice skating rink, where the ice is as smooth as you will ever get on the street, and found out why studded tires aren't the enormous gain that you might think:
Considering that only about six studs are in contact with the ice at any one time as the tire rolls across its surface, we found that the weak link is the ice itself, which chips away during contact with the studs. The ruts left on the surface of the ice showed that the studs were making contact, but the ice itself just wasn't strong enough to be considered a good traction partner for the tires.I suppose at -20 degrees, the ice would be sufficiently strong that the studs wouldn't be braking the ice so easily--but at -20 degrees, I understand that a lot of tires work okay. Remember that the reason that ice is so slippery is that as you roll across it with a tire, the pressure causes it to melt, forming a thin sheet of water. When it gets cold enough, the pressure of your tire isn't going to melt so much of the ice.
Another issue is that when you start to skid, you are not supposed to brake--but to turn the wheel in the direction that you want to actually go. Of course, because I don't have a lot of experience driving on ice, when I started to skid, I did what makes the most sense on dry pavement--I stepped on the brakes. When you turn your front wheels intead away from the direction that you are skidding, the tires are both resisting your motion towards the ditch, and because they are getting some traction, you have some hope of ending up staying on the road while you are losing speed.
Unfortunately, the only way to do the right thing under these circumstances is to get experience skidding in a controlled environment. That's true with other aspects of driving as well. That's why the more practice you get, the better you are at driving. Like many skills involving muscle memory, you must do them regularly to become proficient.