As a native Floridian who grew up in the sandy hill region of Central Florida, I know all too well that lowering your tire pressure works wonders when driving through sand. More than once, we would lower our air pressure down to between 15 to 18 psi and pull through with no problem whatsoever.
But you have to have flexible sidewalls on your tires. A heavy six or eight ply sidewall will not allow the tire to "squat" or "spread" on the surface. We would always run regular "car" tires on our trucks for this very reason, when you let out the pressure, the tire would spread and off you would go and we never had four wheel drive.
It works well in bottomless sand, but sand isn't "icy." So I suppose it depends on what kind of snow you're trying to drive through.
Keep in mind, the concept of lowering pressure for sand is to spread the contact surface of the tire on top of the sand. A tire with rounded "edges" works even better and a lot of fellows would run oversize rims, (wider, not taller) on the back of their trucks. When radials came on the scene, this worked exceptionally well.
Another thing to keep in mind when driving in soft sand is not to spin the tire, but to keep the vehicle moving right on the "edge" of spinning. I believe this is what snow driving and sand driving definitely have in common.
As far as adding weight is concerned, that always worked well in sand. Sometimes, if we got good and stuck, we would simply lower the tailgate of the truck and shovel it full of sand. That would give us enough weight that we could then pull out of the hole. It's the reason the rear tires on the soon to be world famous "LUV" Machine are filled with water which enables me to drive anywhere on the farm without getting stuck.