OK, all this talk about tipping over makes me wonder. If on a steep hill crossing horizontally lets say for arguments sake that the top of the hill is to the left of the tractor. If the tractor were to start tipping over to the right, which way would you turn the steering wheel to possibly avoid the almost tipping over problem. This is assuming that the tractor is just feeling tipsy, not already turning over. Just wondering in case I ever get that deep into this situation. My spidey senses usually warn me and my cheeks start pinching the seat wayyyyy before I ever get to that point.
To the OP's original question:
Lots of (VERY valid) exceptions to what I'm about to say were raised in this thread, e.g., if there's a large wood chuck hole on the LOW side, or a rock, etc..., on the HIGH side, things might require a different solution. And the whole "take a TIME OUT and THINK" approach (if time allows) is certainly worth it's weight in gold.
But, in the OP's original hypothetical, with all other things being equal (meaning, a uniform terrain, hilltop to the left, low side to the right) and the machine starts to feel "light" on the UPHILL side:
TURN DOWNHILL.
I know this from garden tractors, ATV's, snowmobiles, etc....
And if you think about the converse, possible reaction (i.e., turning uphill) it may help. Specifically, if LEFT is UPHILL, and you
were to turn LEFT, an ATV's Center of Gravity would shift to the RIGHT, RAISING the "inside" (i.e., the UPHILL) wheels, in a LEFT turn.
This is the OPPOSITE of what you want, if the DOWNHILL side is to your RIGHT.
You want the uphill wheels to get HEAVIER, not lighter.
So, with the hilltop on the LEFT, and you're feeling "tippy, TURN DOWNHILL, which would be to the
RIGHT.
Now, I didn't say "ALWAYS turn down hill"--even though I wanted to) because, as someone mentioned, if there's a washout/diversion ditch/huge woodchuck den, etc..., you could turn downhill and fall into a HOLE, leaving you even worse off than you were before.
But,
given evenly sloping terrain, with no holes/rocks/logs, etc..., and the UPHILL side gets "light," TURN DOWNHILL. In the OP's scenario, with the UP-side on the LEFT, turn DOWNHILL, to the RIGHT.
You asked a good question. I hope that helps.
My Hoe