I don't have the experience of a lot of guys on here, but see no one else had bitten yet, so thought I'd give it a try.
I've helped a friend of mine for a few years that has the contract on some land leased by the Conservation Department here in MO. Two areas have pretty steep hills. On is actually roadside embankment probably 30 feet high, the other a hillside or perhaps half an acre or so. I've mowed both with his 61 Encore Prowler, and my Gravely 250Z. If the grass is wet, you can have some problems, but if the grass is dry, it is amazing where they will go. I was pretty reluctant to try the hills at first (bravery is not my strong suite), but once you get familiar with the machine, you will learn how to control it.
Perhaps the main thing is remembering to work the controls SLOWLY. Any sudden surge in power or direction change can cause you to lose traction. On a reasonable hill, if you do, all you will likely do is slide sideways anyhow, but it is a little scary. Going across hillsides, you just learn to keep a bit more power to the lower wheel than to the top, as you have no steering on the front. I do believe some models allow locking of the front casters, which, supposedly will give you a bit more control on slopes. Probably the least controllable is going down hill. Any attempt at braking can cause you to lose traction if your tires are worn, or the grass and/or ground is wet. Hope this helps. Neill