Originally Posted by WaterDR
Lowering the pressure increases the amount of tire touching the pavement and thus better traction.
Not where wet roads or snow covered roads are concerned. On wet roads, fatter/lower air pressure tires are like water skis vs. snow skis... wider means the tire will hydroplane/ride on top of the water more readily. For wet road conditions where hydroplaning is a possibility, you want to be fully aired up. The lower the air pressure, the more likely it is you'll hydroplane.
The rule-of-thumb used by pilots for the speed at which when aircraft tires will hydroplane on wet runways is 9X the square root of the air pressure. So if a tire were at 25 psi, it would tend to hydroplane at 45 mph. If the tire was at 36 psi, it would tend to hydroplane at 54 mph. That is a good illustration showing that the higher the air pressure, the higher the speed it will take the tire to hydroplane at.
For roads with up to a couple inches of snow, narrower tires can dig down through the surface snow to the better traction of the pavement below. That's why in areas with lots of snow like Alaska you'll see tall "pizza cutter" tires.
Same with icy roads... wide fat tires will lose traction on ice far more readily due to the reduced pressure each square inch on the tire has against the ice. Like an ice pick (tire studs) has great traction on ice but not a flat frying pan (wide tires).
When you want lower air pressure in snow is when the snow is deep & you need to be able to stay on top of the snow like when you're offroad in deep snow.