A horse can’t climb!?!
Having caught several horses I have found if you are near rocks when they fight you they will climb!
As long as there is some grass and it’s not too steep you can get a horse up some fairly high places!
Aha! Always register a horse asap, much easier!
Tip-look for a horse with a longer mane than the others, they seem to be faster, and a solid coloured horse, altho they are harder to tame!