I'd take a guess at most people not being stupid enough to take a bike out in snow and ice.
I however am.
There aren't any proper winter tyres so what you look for is compound and tread pattern. My tyres are designed to "switch on" at low temperatures and have a semi off road tread pattern allowing it to cope better with grit and snow. It will still not grip on sheet ice and I won't even try it. Snow... yet to find out. I went on off road reports which stated these cut through the dirt properly so here's hoping. I've used all manner of tyres on snow. It's just a matter of slowing down - the tyre type determines to what degree.
Those are Michelin Anakee 2s but there are quite a few more off road tyres which should work in snow.
Most bike tyres have an amount of silica in as it helps grip in the wet. What you're looking for is those that advertise a high silica content along with the appropriate tread pattern. If you get what are basically cut slicks you'll come off just on the grit they put down as they go over the top these days anyway. This is ignoring them dropping heaps of the stuff at junctions and on roundabouts where they're going slower which I don't ever remember them doing before.
You can however do the opposite of deep tread and 'low temperature' tyres. I did an emergency, very high speed ride on "track day and hard road riding" tyres which had a reasonable tread on one christmas day. The gritters had not been around and there was ice all over - I passed one or two cars embedded in signposts.
To give you an idea of how hard I was pushing it, thrashing the bike on this route in the height of summer with all green lights took me 28 mins. I didn't get all green lights and did it in 32mins. I went over ice, and full pelt round roundabouts with no problem. Granted I straight lined it over the ice and was lucky but still.
What this shows is that some tyres which are very, very soft (a light 400cc did a rear in under 3000miles) with a high silica content will stick in winter even though they're for fast summer riding. It's all down to researching the compound used and thinking very hard about whether this is really suited.
I doubt many manufacturers will advertise "winter" tyres as frankly that encompasses everything from the warm rainy conditions of today to solid ice and they'll just get sued.
EDIT: I'm a little pished by the way.