If you go off of even the tiniest ledge with a horse it puts the horse in the fall animation and puts your movement to a 100% stop. A while ago there was a change where dashing with classes were given a greater fall distance off of ledges so that it didn't stop them and put them in a falling animation from even the tiniest ledges. This needs to be applies to horses in general. If you so much as go off of a small rock  in a field, your horse stutters and all speed is canceled. 

Are you referring to Caution?  Try locking Caution on your horse.