A buddy of mine helped run the Michelin ice driving school in Steamboat Springs, CO for several years, and this info comes from him and their research with Michelin.
For a given tire size, having a greater percent of the footprint be rubber (vs voids) causes a lower PSI in the tire footprint. This reduces the creation of a thin layer of water atop ice from pressure as the tire's weight bears down on it and creates momentary "heat". This layer of water happens on hardpack snow as well, and is really what reduces the available traction dramatically. As noted above, ice deforms to the tread a bit as you pass over, but the water layer can offset the gripping edges traction significantly.
So, Michelin's ice tires (Alpin, Alpin Pilot, etc) have smaller voids and large rubber surface area. The softer rubber compounds at low temps have been covered above, and they further reduce pressure areas by easily conforming as the footprint passes over. Of course, the treads also have a lot of siping edges for mixed conditions.
The worst tires on ice are traditional snow tires with their huge voids. Next would be a modern mud tire for the same reason. I drove on studded siped mud tires for years out here and had great luck, but on glare ice they were not ideal. He explained why. Turns out the studs provide an improvement of grip on ice, but also create a circle of rubber around the stud that is not firmly in touch with the ice for a bit of an offsetting loss. The net effect is an improvement, but some tire dynamics impede. He suggested attention to proper tire pressure was critical to let the studded area deform, and noted that truck tires with studs don't deform as nicely as "softer" studded car tires. The LT tire carcass is too stiff to allow the studs to be pushed in a bit, where the passenger carcass will - restoring some more rubber into contact while retaining the grip of a stud buried in the ice surface.
On the other hand, the Alpins on my Subaru seem to be too extreme in lacking voids. They're incredible on ice/packed snow, but evacuate poorly on slush and deep snow at speed. The Alpin 4X4 on the 80 has a much more open design and is incredible in every condition I've encountered.
He noted that these newer studless designs are far superior in typical emergency conditions like we all see on The Weather Channel footage - ice glazed highways or a huge patch of ice coming up to a stop sign. Frankly, that's my worst case scenario too. They are also superior on a hardpacked snow road. When you get into deeper unconsolidated (untracked) snow (more than 3 inches), the advantage starts to shift to a mud tire/ traditional snow tire configuration. For typical suburban road driving (plowed or tracked snow), best service is from studless.
It was an interesting conversation (2 hrs) and led to me replacing studded muddies last Winter with the new studless designs.
Doug