According to Motortrend.com:
“It's best to replace all four tires with winter tires because differences in tire size and wear can negatively affect a car's handling and stability." “A modern snow tire can provide up to 20 percent better snow traction than an all-season design. We've verified this from behind the steering wheel. A well designed winter tire provides a tangible seat-of-the-pants performance advantage over all-season tires in both snow and ice conditions. This includes better initial hookup, shorter braking distances, and cornering that's both more predictable and controllable. This is important, since again according to Goodyear, “The largest group of [winter] accidents results from loss of lateral control of the car on ice and snow."
According to msn.com:
“What is most important is the level of improvement winter tires
offer over standard all-season tires. Even at 15 mph, in tests we
conducted on an icy surface, the vehicles equipped with winter
tires stopped from a half to a full car-length shorter than
identical vehicles on all-seasons. That could be the difference
between a safe stop and a bumper-basher at a traffic light. At
higher speeds, those differences get more dramatic."
“…similar improvements were apparent negotiating a loose slalom
course—not unlike typical parking lot maneuvers. Not only were the
vehicles on winter tires measurably faster (by 10 to 20 percent)—an
indication of the added margin of traction they provide—but also
they were noticeably easier to control."
“One of the keys to that performance improvement was the fact that
those vehicles were equipped with four winter tires, not just two.
Because of the significant differences in traction between winter
and all-season tires, it is imperative that they be installed on
all four wheels. Otherwise, the two ends of your vehicle can
experience different traction characteristics, resulting in
potentially dangerous instability.
According to Forbesauto.com:
“Even in all but the harshest of snowy conditions, a two-wheel-drive vehicle (whether front- or rear-driven) will perform safely and securely in snow with the proper snow tires mounted on all four wheels. Comparison tests performed by automotive-enthusiast magazines in the snow have shown that a 2WD drive vehicle with snow tires on all four wheels will outperform a 4WD vehicle with regular tires."
According to the Tire Industry Association:
“If winter tires are installed on the front axle of any vehicle, they must also be installed on the rear. The difference in traction qualities may result in adverse handling characteristics, which can lead to loss of vehicle control. Therefore, in order to maintain performance and stability, winter/snow tires must be installed on all four wheel positions on front-wheel drive vehicles."
According to Consumer Research Advocate:
Though you might be tempted to buy just two winter tires for your drive axle, every expert we found says this isn't a great idea. That's because mixing winter and all-season tires can lead to poor handling balance. The Toronto Star's John Mahler says that this strategy can be dangerous in skid situations, as the front wheels get different traction than the rear wheels. All experts say four winter tires are your best bet, and even inexpensive winter tires will do better in ice and snow than all-season tires.