Want to get around easy get some wheels/tyres with no profile they scoot around in the snow (less surface area)
Im guessing you meen higher profile and less width.
The contact area/surface area is the same but its the shape of this contact area to the ground that changes(if the weight and pressure is the same).
Rather than been wide(left to right) and narrow(front to back) (helping cornering grip) less width (left to right) increases the (front to back) size which helps traction but the contact size and area stays the same its just changed shape.