http://blog.bookviewcafe.com/2011/01/24/down-and-dreamin-a-photohorseblog/
Offered for your information should you ever need same when writing a story that has horses in it.
You can get problems if a horse stays down for a prolonged period, because their digestion and circulation both partly rely on being upright on all four legs. But laying down for a few hours "just because" is perfectly normal.
Lying down in a confined space or up against something can be a problem too -- the horse can get "cast" ie. unable to roll to where it can get its legs back under itself. Then someone has to drag or roll the horse into more open space so it can get up (and avoid getting their head kicked square in the process).
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Friend had a ranch horse with some odd ideas... Habibi would steal your shirt if you hung it on the fence. He'd also grab cats and carry them off into the hills. The bedraggled cat would come staggering back 2 or 3 days later, but the shirts were seldom seen again.
However there won't be a posterior for posterity.
[This message has been edited by LDWriter2 (edited January 27, 2011).]
I am focusing almost completely on sci fi now, and am planning on NOT having any horses in those stories. If you get a minor detail wrong, the horse purists are watching
Just put in a disclaimer that any difference between horses in your science fiction and horses in reality is due to genetic mutation.
The book on her site does look pretty interesting, I must admit.
But my personal pet peeve in SF/F is climate. Now, I've lived and worked outdoors in both extremes, arctic-calibre winters and desert summers, so I'm pretty familiar with life in both... but 99% of the fictional characters consigned to either... are dead. They've died of exposure, one way or another. The author describes conditions I know requires NN-gear to be comfortable or at least XX-gear to barely survive... and fails to give their characters either. You don't just put on gloves to cope with -40F and a blizzard, and you don't just carry a canteen to cope with +120F and unremitting sun...
But hey, it keeps the corpse-pickup crew employed 
Well, of course. Didn't Roddenberry himself describe ST as "Wagon Train to the Stars"?? Brust was just takin' him literal-like.
Now that I've posted my qualifications, the lady who wrote about horses laying down is right on the money... Buuuuuutttt I'd like to add a little that she left out:
Not only do horses lay down, but when a group of horses wants to snooze, one horse will always be on guard duty just in case some sneaky predator wants to try an attack. All the other horses in the group can lay down and snooze except the one on guard. Then, if the one on guard feels the need to sleep, he/she will nudge one of the snoozing horses awake to take his/her place so he/she can lay down.
One time at a horse show, I had to get my horse ready for an upcoming class. I found him sound asleep on his side in his stall in the barn. He must've been sleeping pretty darn sound, because it seemed to take forever to wake him, and then he didn't know where he was. He finally did get his wits about him and get up, but this was the only time I ever had this happen.
And, yes, I have seen a horse dream a couple of times. If you think it's weird when a dog dreams, you ain't seen nothing .
There was a SF TV show with horses, some episodes anyway. Kinda funny to see spaceship pilots and engineers usually zipping between stars riding a horse like they had done all their lives.
Otherwise, i'll follow ejs's recommendation and blame it on a genetically-mutated camel.
(Fyi: Gallopping on a camel is like riding on a bumpy cart with oblong wheels where your body heaves fore and aft while the beast foams at the mouth. I think I may prefer space travel, but am yet to try it... one day.)