Keep in mind you have a 1 ton truck and all the weight is up front (and the plow just adds to that), leaving very little in the back, so there isn't enough weight to force the tires to get traction.
My 95 3/4 ton with a V10 is absolutely worthless in the snow in 2 wheel drive, even with new tires on it. If there is snow on the road, it's in 4 wheel drive.
You may just be in a learning curve here, lol. Put 2500 pounds in the back, and your problems will more than likely disappear. When I had a pallet of salt in my bed I too could run in 2 wheel drive until I got to using the salt up.