Snow Tire Wraps for Bicycles In some areas of the world, cars are allowed to use snow chains (or cables) in order to increase traction on ice and snow. This is slightly complicated on bicycles, but has been done. The main problems seem to be the chain being fixed to the tire while avoiding the rims (for brakes; presumably this can be relaxed for bikes with disc brakes to grab around the rims). 

As an alternative to installing tire chains, various manufacturers have been selling snow socks (wraps) for car tires, which are temporary stretchable covers for your tires designed to increase traction in winter driving conditions without having to install chains or specific winter tires. While I haven't used them, they seem to be helpful for occasional cases where all season tires are not comfortably enough. It seems like some of them work on changing texture due to water absorption due to tire heating (which I don't think will happen on a bicycle, but depending on absorption rate, could be pre-treated with warm water before riding), while others start textured. 


Does anybody offer snow socks for bicycles? (I was not able to find them, but I'm guessing you could stitch together a set for both tires from one car snow sock, possibly with some additional fastenings to prevent the cover from rolling off. I also did not see a similar product for motorcycles.). 
If they exist: Has anyone tried to use snow socks on bicycles? If so, did they offer a significant advantage over running a smooth road tire or a non-smooth commuter tire such as this (or alternatively, some knobby variety of tire) without the sock?
If they do not exist: Does anyone have some theoretical insights to the last problem?


I realize there are two issues here - snow and ice, which are related but somewhat distinct due to the types of snow and ice, so characterizations in both cases would be useful. Snow socks are useful for on-road use, so lets restrict the answers to the case for on-road use.

This question is primarily of theoretical interest, given the installation times for snow chains being longer than a tire swap, but snow socks should be quicker if they can be fastened to the tire around the rim as in the disc brake case.
You can avoid this problem altogether with studded tires



The pattern is deep enough so that it grabs quite well on the snow, and the studs give you a very good grip on ice and hard snow. On uniformly flat ice, the grip is almost as good as asphalt.

If the tires are good, you can wear them for all winter season, even if there is no ice. The studs are not very prominent, so the whole tire is still in contact with the road. This solves the problem of having to adapt to weather conditions. At my local bike store they assured me they would last for at least 5 years.

Source: I have tires like the one in the image in the Swedish winter.

PS: here, I have never seen cars them using chains or socks, they have winter tires instead, pretty much a car version of the image. Not all have studs, though.