I just wanted to add a few little things to the sensible points above:
- Not all summer tyres are the same and not all winter tyres are the same. Some Summer tyres are really bad on snow (I think, maybe, primarily the ones that come from the countries, such as Germany, where Winter tyres are 'de rigeur' and Summer tyres aren't expected to ever see snow) and some Summer tyres are merely 'not so good'. Equally, the cheap Winter tyres tend to be less good than the expensive ones, and while even cheap Winter tyres can be ok on snow, that's not all that you are expecting them to do - you will likely leave them on for the coldest three or four months of the year, and they will be expected to cope with all the conditions that occur in that time, and those conditions will include more 'cold and dry' and 'cold and wet' days than actual snow. This is where the cheap Winter tyres often fall down - performance on the more normal conditions. (Of course, ignore that if you only fit them for a couple of days when someone has actually Tippexed out the landscape - changing tyres just for snowy days is a pain, though.)
- In 'Auto Express' (warning: a video) they also had success, surprisingly, with a 'spray'. Now, tyre compound softener sprays have been existing for quite some time, but I was as surprised as they were that the spray they tested gave a big improvement. Softening the rubber must have an impact on wear, but I'd hate to guess how much. Like the 'sock' could be a worthwhile last ditch (sorry!) measure, if you don't find the ditch before you apply the spray.