I don't think a skid on those slopes makes much sense at all. There's very few SSLs I can think of that'd be able to run an attachment while clawing up that steep of an angle.
CTLs... I wouldn't run a CTL (or SSL) *across* a 45 degree slope. If the slope is short, you may be able to get away with running up/down it, but that also means a lot of turning at the top and bottom of the hill. As digdeep said, there's also an issue with oil starvation. Most manufacturers recommend avoiding prolonged operation at greater than a 2:1 slope (varies, of course, by manufacturer). Even if the machine seems planted going up and down, killing an engine probably isn't worth it.
If you want to try it out, look at ASV and Deere machines. They tend to be have better weight distribution than Cat, Case, or Takeuchi (all of which are rear-heavy). If machine operation at slopes of greater than 45° are permitted, demo it and see how it feels in the seat of your pants. My personally, I'd be scared s#$(less.