Reading the thread title, my first thought was the Duratrac but it sounds like that's a no-go. I'm running the Cooper STMaxx on my '06 Dodge 2500 deisel and thought they did great last winter though never got into any real deep snow. They have 3 sidewall plies and have a good reputation for wearing well and holding up off the highway. I have 18k on mine and am happy with them so far...
I also like the Coopers. I tried the Dura Track on my 2500 Ram Diesel, and they have too soft a side wall. Even at max pressure, with a heavy load,you can feel the side wall roll on curves. Without a load ,I could not see them doing any better than any other snow tire.The Coopers are not as expensive and a better tire IMHO.
I suspect your claiming the truck goes from side to side is the posi-traction/limited slip. An empty bed pickup is about useless in snow if you don't have 4wd. If I put 1500 pounds or so in mine,it will push about any amount of snow until it high centers
