Putting the last few posts together says that plowing is based on momentum - the combination of weight + speed. The less weight you have, the more speed you need. Hence, an ATV needs a fair amount of speed, where as a huge loader doesn't need that speed. And, a truck is somewhere in between.
All of which suggests that the size of your tractor has a lot to do with plowing technique.
You can overcome the issue with traction. Traction can come from aggressive tires/chains, or from weight, or both.
I plow my (level) driveway with a
BX1500 - about a light as a tractor can get.
I have also driven it up a fairly steep, icy slope, which I can't explain, but it worked. Turf tires, too.
Actually, turf tires will be better on ice and hardpack snow (not better than chains, but better than more agressive tires) as there is more contact area. Big lugged tires get traction by biting into the material. You can't bite into ice - unless you have chains.
So, as others have suggested - get some chains, but first see if you can do it without.