You can't really ask a horse how he or she is feeling - but they do do their best to communicate with us.
However, there's strong evidence horses can suffer from depression - and suffer from it in the same way as humans.
A depressed horse will stand still for long periods of time with the head and sometimes ears drooping. They often show indifference to both humans and other horses, and may ignore "interesting" objects. Studies indicate that lower blood cortisol levels are also associated with depression.
Also, depressed horses will often go off their feed and may show a lack of interest in treats they normally like or activities they normally enjoy. Just like humans!
Depression can be a sign of mild illness or pain. It often occurs after the loss of a long time buddy (pining). It can also be caused by forcing horses into activities they don't enjoy or by not letting them do things they do enjoy. (Sometimes the cure for depression is to go out on a nice trail ride every week or so). Horses that are kept entirely alone are almost guaranteed to become depressed (with rare exceptions).