I have not had a horse in several years but it seems to me that only young foals tend to lay down. I believe I have been told that horses have a hard time breathing when they lay down and that this could be a sign that the horse is in distress. I could be totally off base here. Somebody please correct me if I'm wrong.

I've known horses that always sleep on their side. I was taught this is a sign they have enough room and are comfortable enough in their stable to trust laying down. Since horses are prey they don't often lay down if they feel threatened without someone else in the herd to stand guard.

I always was told the same with the hard to breathe issue, think about it thats a great deal of weight on their ribs and lung area let alone when they are standing around all the time too. I have seen some on their sides but not for very long.

Horses must lie down to reach REM (http://en.wikipedia.org/wiki/Rapid_eye_movement_sleep) sleep. They only have to lie down for an hour or two every few days to meet their minimum REM sleep requirements.[10] (http://en.wikipedia.org/wiki/Horse_behavior#cite_note-Horse_sleep_pt._2-9) However, if a horse is never allowed to lie down, after several days it will become sleep-deprived, and in rare cases may suddenly collapse as it involuntarily slips into REM sleep while still standing.[12] (http://en.wikipedia.org/wiki/Horse_behavior#cite_note-11) This condition differs from narcolepsy (http://en.wikipedia.org/wiki/Narcolepsy), though horses may also suffer from that disorder.[13] (http://en.wikipedia.org/wiki/Horse_behavior#cite_note-12)
from http://en.wikipedia.org/wiki/Horse_behavior#Sleep_patterns

I would have to agree, I've known several horses who would sleep through the night in their big box stall. It is when they lay down and are unable to stand or strain to do so that they are most likely in distress.

The problem with horses lying down for any length of time is that their weight stops blood flow to the muscles that they're lying on, and without blood flow those muscles start to die...