Originally Posted by Howl
Under-inflated tires will grip rough surfaces better, but 95% of winter driving is on hard pavement so its largely a moot point. If you're driving on a rough, snowy road and are worried about grip it's a valid tool at your disposal, but you have to remember to re-inflate them once you get back on pavement.
the thing is, as wear patterns demonstrates the force is exerted on the outside of the tire while the inside cups (which is why you get that wear pattern) therefore your effective surface area is actually less than a properly inflated tire. They aren't like bike tires which will sit pretty much flat if the air is deflated from them. You want your tires to lie flat on the snow not cup and have pressure points along the outside of the tire which will reduce traction. If you look at the picture I posted of the way the tire wears when underinflated this happens because the force is distributed to the outside of the tire where as very little force (and traction) occurs at the center of the tire, therefore you reduce your footprint and subsequently reduce your traction).
Also at normal inflation the tire will cut through the snow which is what you want. If underinflated the tire will tend to float on top of the snow which reduces traction further. This is why you underinflate on sand because you don't want the tire cutting into the sand you want it to float on top.
I've also tested this empirically (not by choice but due to corroded wheels that wouldn't let the bead properly seal) and you definitely lose traction when underinflated in the snow and on top of that the car becomes squirrely and responds differently with the deformed sidewalls of a low tire.
edit: here is pic of what your footprint looks like with different inflations
double edit: and to be honest whether you believe yourself or me to be right it doesn't matter, underinflated tires are very dangerous under normal driving conditions and should NEVER be recommended.