Winter tires work better on the snow because of the deeper grooves so that it can dig deeper in the snow so more of the rubber can be in contact with the road, therefore increasing the friction.
The coefficient of friction of rubber tires on wet snow goes from approximately 0.3 - 0.6. Using the different coefficient of frictions, we can see how winter tires work better by allowing the car to stop in a smaller distance, making driving in the winter safer. We can split the friction into translational friction and rotational friction.
A car traveling at 25mph (11.176 m/s) with winter tires with a coefficient of friction of 0.6 goes a distance of 10.61m.
A car traveling at the same speed with all season tires (coefficient of friction of 0.3) goes a distance of 21.2m.
The winter tires going the same speed as the car travels a distance of 5.31m. The all season tires goes a distance of 10.61m.
Notice how the wheels stop halfway before the car totally stops, therefore the wheel is just slipping and not rotating at that point.