While you may have great tires, when you need to drive in snow and ice, having snow tires is vital to traveling safely in this type of weather. The importance of winter tires can be seen when you start driving in precarious situations and your vehicle is sliding all over the road. Snow tires will do more to grip and grab at the ground rather than the smoother riding regular tires.
The snow tires are made of more flexible material to not crack and become brittle in the cold weather. Regular tires are made to withstand the heat and the harder roads while snow tires are made to give a bit more while being able to grip the road. The treads are bit wider and deeper so when they hit the snow or slushy conditions that can cause vehicles to slide, the tread can absorb some of it.