You're waiting your turn in a show or class and realize your horse is dozing off. Why would this happen?
1. The horse has narcolepsy. This is rare in horses, and there's no good treatment for it.
2. The horse didn't get enough sleep last night. Sometimes horses with stable vices will keep themselves up all night. Horses that are anxious and nervous and don't feel safe may not lie down to get their REM sleep and may be sleep deprived.
3. They're so bored they decided they might as well take a nap.
Number three is not a problem - a horse that's napping while waiting will properly lock its leg. A horse that has narcolepsy or sleep deprivation, however, may well collapse under the rider, especially if they're deprived of REM sleep. Sleep deprivation can often be treated with environmental changes or medication to help an arthritic horse lie down and get back up.
Equine narcolepsy is incurable and there is no good treatment for it (although an antidepressant called amitriptylene shows promise). It's possible to manage the condition, but a horse that regularly falls suddenly asleep during work because of narcolepsy should not be ridden.