A few comments on this thread.
Yes, snow tires do make a difference, in most Winter weather. Buy quality, not cheap ultra low price point tires.
Don't put them on too early or leave them on too long. You can destroy a set of winter tires in a month or two of warm/hot weather driving. Soft compound and tread patterns will not stand up.
I know winter tires are not cheap, but, avoid buying used. You have no idea of the history of the tires. Unless you know what to look for they could have been repaired. BTW it is illegal to repair a flat tire with a plug from the outside.
When you change from summers/all season to winter, PLEASE make sure that wheels are re-torqued after 100km or so. Most tire stores and dealers will do this at NC and it only takes a few minutes.