Airing down tires like what your talking about will be mostly for the ride. If you have big enough tires, airing them down will help float you in the snow. On a normal or slightly larger pickup tire, airing down will allow the tires to flex more for better grip and flex better going over rough terrain. Larger tires will allow for a bigger foot print and give less weight per sq in. If you take a tire to low, it could be easy to roll it off the bead. Going down the road with low air pressure can crate heat, heat in a tire is not your friend. Normally you don't go down a rough road or snowy road fast enough to create heat enough to hurt an aired down tire, however going down pavement, depending on how far and fast you drive, that will build heat. I have drove into town with 3psi on my 37x14.5R15. I wasn't going crazy fast but not stupid slow and all was fine. The larger the tire, normally the less pressure. So a normal pickup tire, stock sizeish, say max 60 psi on a normal pickup, I wouldn't really ever go less than 20-30psi. Mine are 80psi max, during hunting season I will go to about 30-35psi for the whole season.
