I live and ride the mountains of the west, So we have to go up and down some pretty steep mountainsides. Going up I try to zig and zag so it's not so much work on the horse. Often down hill, It's easier to go straight down and let the horse get his hind feet up under him to work.
Some of my decision is based on how much vegetation is on the ground that might tangle the horses legs and How muddy and slick the ground is.
Horses can't fly. So going off near verticle is not an option.
If you look in the top-center of Painted's second pix you'll notice a couple of horses coming down a pretty steep slope. Looks like a pretty loose surface, too, which probablymakes it a bit more of a challenge.
Painted always has beautiful scenery pics. Envy...
I judge the hill by my comfort level, learned through experience. I find it's actually easier to ride up and down steep slopes than have the horse beside or behind me worrying that he might have to place his foot where I am in his way. When I was a kid, we rode up and down the ski-hill until the snow hit. Ours horses were in great shape!
We call our horses mountain goats because of the stuff we climb. There have been times when I was not sure we would make it all the way up or when I look over the side of a hill my heart starts to throb but my horses just sit down on their butts and slide right on down. We do have a Mule that we ride with quite often and it is said a Mule will not do anything to hurt itself so if we are unsure it is too steep when trail blazing we will see if the mule will do it. If the mule wont go then we know its too steep...