Indeed. The first thing I do when buying a second-hand car (I never buy new cars, what a waste of money) is to buy the best winter tires (and summer tires if needed) that money can buy (lots of that available, as I save so much on the car). I never have any problems in any conditions (and there are a lot of "conditions..")
All seasons tires are rubbish. Also the "new" ones (re sister comment).