I'm really starting to get into this thread. haha
I think that horses do mourn, people, other animals I think when someone leaves who they love then they grieve.
A year ago my mare lost her "boyfriend". They were in the same herd and did everything together for the past eight or nine years. They weren't herd bound in the slightest to one another and never had a problem leaving the others side because as soon as they were together again they went off together. He was dying and we brought him up to the barn so that the vet could look at him and my mare busted through six fences and a gate to stand by his side. She wasn't tethered or haltered at all and in an open area where she could have just run off. When he was being put to sleep she stood over him, laid down with him and when it was all said and done she didn't leave his body for days, didn't even wander out of the property line. When she went back into the field she just walked around and looked like she was mourning. If I had any doubts that a horse could mourn death than she cleared it all away from her actions.
If a horse can mourn a horse then can't it mourn a human as well? As people we mourn the loss of a dog and another human it may not be as drastic or the same but it's mourning. Also everything grieves differently. I think certain horses can mourn the loss of a person and not show it at all while others make it quite obvious. I know I've had several instances with horses and other animals that have made me think that they do grieve and have their own sort of funeral for the deceased. I've seen horses stand over the grave where one was buried and just wait, I watched a horse where we boarded lose his owner, when they carried her body out he followed the ambulance down the lane and was disconsolate for quite some time, and I've seen horses wait for their people and won't move until their person arrives.
I do believe that a big difference and maybe why we question if a horse mourns is because they continue on with their lives. (As harsh as it might sound). I've noticed that in humans when a person dies it takes a bit longer than it does a horse to accept the death and move on (not in a completely normal sense but in a "as best we can" sense). Horses (and animals in general) seem to realize better than us at times, that death is an inescapable fact of life. They seem to know that they need to reflect on the good times and continue living life to the fullest because eventually it will be their turn. Just my thoughts.