If your tire does not break through to a solid surface, you will not get traction on snow regardless, unless you are using either absurdly large balloon tires, or a tracked vehicle. More pressure ensures that any knobs or studs or treads have the best chance possible of finding traction.

Interestingly, lower pressure and higher contact patch does not actually reduce efficiency on dry asphalt either. This is because elastic tire deformation is highly elastic, but the increase in rolling friction is small. In contrast, overly stiff tires convey more vibration into the frame, which is lost as heat, instead of being conserved elastically. Even on perfectly smooth indoor tracks, just they hysteresis losses from pedaling on an overly firm tire add up significantly.