Horses that were not raised on uneven terrain just don't learn how to watch out for their feet. They can learn, but it take some riding for them to watch and take care of their feet. Along the way, you will have a few trips and a few rock bites on thier pasterns as they learn.
There is a ranch new me that raises quarter horses on the side of mountain. Each suumer they have a sale. The horses are highly sought after not ony for their breeding, but because those babies grew up following their mares across some really rough stuff. Those horses have a reputation of being really sure footed the rest of their lives because of what they learned as foals. Same thing with most mustangs. Owners rav about how sure footed they are, because they learned as babies to watch their feet.
My current gelding grew up in the grass pasture behind the house. And the first year or two of trail rides, my daughters teased about him being an Oaf. Tripping and Clumsey. But a couple of years of trail rides and he is pretty sure footed now.
I'm riding my horse, but turned around and taking pictures of the riders behind me, and not worried about what we are crossing.
He will even work his way through the blow down, picking his feet up and watching where he puts them