As Graham says, no tyre (other than a studded one) is going to be great on ice, but a winter tyre is clearly still going to be considerably better than a summer one.
I can assure you that with decent winter tyres fitted I have managed to drive (albeit gingerly) on icy (melted/refrozen) roads up in the mountains when there is no way that summer tyres would work.
The whole business of salting mountain roads is quite controversial with the locals as the salt melts the snow, but then once it gets down to -15°C or so that melted snow refreezes as sheet ice. So for those with proper tyres fitted, just snow ploughing is a better solution; leaving a "route blanche" with reasonable adherence rather than creating an ice rink.
