Yep, you've got the idea. The snow condidtions change all the time on the mountain, so some days the snowcats may not be able to climb even moderate slopes. Somedays we can get traction on even the steepest. A winch cat can almost always make it up a trail.
Gravity is a big deal on a ski slope. All day people push snow downhill, and when we drive snowcats down, we also move a lot of snow between the tracks and the tiller. Half my job involves pushing snow back up with the front blade (thus why its a 12-way, I need all the control to match the slope). The steeper the slope, the less snow I will be able to push up, but it's the steeper slopes that need the most pushing, so we use the winch cats to push the snow up. Some trails get winched all the time (to steep to get with normal cats), others just once and a while when it gets too thin at the top.
Some slopes may be too steep or too soft for us to get good traction and we end up sliding down. It's hard to make a good pass with the tiller when the cat is sliding, so usually a winch cat will come in after and clean up the mess.
As a side note, the winches are all computer controlled. You can actually dial in how much pull you want on the winch cable. As for what the winch hooks up to, usually it's a steel post set in the ground up top, sometimes its a large tree, other times its another snowcat parked at the top.