I would consider myself somewhat of an expert on horses as i have had them for all of my 22 years, and spent almost everyday of my life around them. I have also shown them competively.
Horses sleep lying down and standing up. However, they mostly sleep standing, unless unusually tired. It is actually dangerous for a horse to remain lying down for to long, because they do not digest their food unless they are standing. This is why when they break a leg horses are almost always put to sleep. They simply can't survive without standing.
Sorry it was so long...get me talking about horses and i can't shut up!