This is something that I unfortunately have some experience with. My daughters mare lost her buddy to cancer, she became depressed. What she did was went off her feed... she just would not eat. She just stood at the gate and stared at where we had Katie buried. She was just not herself at all nothing interested her ... not her favorites treats nothing. It got to the point that I called the vet to have her blood pulled cause she was dropping weight fast, vet found nothing wrong and said we just have to see if she pulls out of her funk.
We ended up taking in another throw away horse... it was only that companionship with Elmo that got her out of her funk and turned her around.
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! :)