We always try to educate drivers about the need for matching tires on all four corners of their vehicle. Ideally, all four will always be the same, but the biggest chance for unstable or downright dangerous handling comes from mixing winter tires with non-winter tires in snowy and/or icy conditions.
You can see our test of a mixed set of snow tires below, demonstrating potential hazards under controlled conditions. Real world experience bears this out. I just heard from one of my colleagues about a customer who needed two additional winter tires to complete a set of four.
The customer came to our Indiana distribution center this past weekend wanting to purchase two more Firestone Winterforce tires for the rear of his vehicle. He had purchased a pair of 205/70R15 Winterforce tires elsewhere and had them installed on the front axle of his front-wheel drive Buick. After having the tail end pass him and exploring a ditch, he came to us looking for two more to complete the set. He is now a convert to the wisdom of 4 matching snow tires.
To see exactly what the customer experienced, watch "Why Gamble With Winter Tire Selection When Four of a Kind Always Beats Two Pair?"
The front-wheel drive car experiences oversteer as the front wheels turn, while the rear wheels want to keep going straight. On a rear-wheel drive car, with snow tires on the rear only, the results are different, but also not good: