Do horses get bored?

As far as I can tell - yes. Especially the smarter ones. Horses get bored if they drill too much on the same thing, and then they will act out. I know a horse who will simply canter off if he's not being asked to do interesting enough work.

Horses like routine in their lives, but they need a bit of mental stimulation and variety in their work, especially if they're in an urban barn and stalled a lot.

Obviously, we can't get in their heads to tell what they are really thinking, but I've definitely seen horses act out to make their lives more interesting, check out, or even fall asleep while waiting their turn to do an exercise or go into the show ring.