Physics
While tire tread and composition are important for traction in winter driving conditions, they do have limitations to how beneficial they are. For example, softer tires do have better traction, but it isn’t practical for a tire to be made out of bubblegum. In the quest for better traction, the question is eventually raised: what about changing the size and width of the tire?
Friction
As torque is applied to a car tire, the rotational movement is transformed into linear movement (of the car) by where the tire contacts the road surface (contact patch). Thus, assuming the tire maintains traction, it obeys the following equation of static friction:
Where 
is the coefficient of static friction, 
is the normal force, and 
(static friction) is the maximum amount of force that can be applied before the tire begins to slip and slide on the road surface. While the coefficient of static friction is specific for a material and is independent of surface area, the amount of normal force is what directly affects the frictional forces of the tires.
Traction
With the coefficient of friction and normal force of a vehicle remaining constant in the majority of situations, it doesn’t seem possible to increase the amount of friction the tires can exert on the road surface. Traction, or the grip of a tire on the road surface, can actually be improved by increasing the size of the contact patch. While this is not supposed to be possible (by the laws of kinematics), it functions on the idea of redundancy. In the real world, the frictional forces experienced by tires are dynamic, not static. Increasing the size of the contact patch introduces more surface area and thus vastly improves the chance of the maximum coefficient of friction actually being achieved.
Tire Width
Intuitively, increasing the size of the tires would also, in theory, increase the size of the contact patch and thus improve traction. In reality, this isn’t the case: changing the dimensions of the tire, with tire pressure and car weight held constant, does not increase the size of the contact patch. Changing from a high-profile, narrow tire to a low profile, wide tire simply changes the shape of the contact patch from long and narrow to short and wide with the area remaining constant.
Conclusion
As discussed, the magnitudes of normal force and coefficient of friction dictate the maximum amount of traction, regardless of tire size, with a given vehicle and appropriate tires. Of course, the real world does not abide perfectly to the laws of kinematics and other physical characteristics come into play such as the size of the contact patch. A larger contact patch increases the chances of the maximum coefficient of friction being achieved between the car tire and the uneven road surface. Thus, with this concept in mind, a wider tire with a larger contact patch perpendicular to the direction of travel does, in fact, improve traction.