I have seen many different sign's from horses with depression. It all depends on the horse. How is the horse in a normal comfortable surrounding and daily lifestyle.
Some horses act like a child having a fit in their stalls, knocking buckets, pawing hay everywhere. Or nit picking in the pasture's at other horses, rushing gaits and such.
I've seen horses pin their ears and just LOOK at you like WHAT?!!?!
Many horses will pace and get angry some will remove themselves from the pack and be alone. You can sometimes just see there expression is sad, ears hung or eyes low. No bounce to their step.
It could be anything. Something "not right" feeling. Helps when you know the horse.
But if you don't know the horse, send him out in the pasture or pen and watch him. Get to know him, spend days observing him, with horses and without. Have someone else handle him, compared to you or the owner.
Sometimes just a evening brushing while talking to yourself with a horse helps them relax and gain a bond they can look forward too each night.
Is he in need of a horse friend? Or a bond with a human to call his own? Maybe his training isnt going right and he just isnt catching on.
Read him, get in his head and learn about him. Every horse is different and should always be treated as individual as us humans are. Plus you learn more and that's always fun! :)