Like humans, horses experience both slow-wave sleep and rapid-eye-movement (REM) deep sleep. REM sleep is thought to occur mostly when the horse is stretched out flat on his side, rather than resting on his chest.
During REM sleep people dream, and its a fair assumption that horses do the same. Their eyes move (obviously, that's why its called REM sleep), and they can make movements, much as sleeping dogs do. Elvis probably isn't dreaming here, not deeply asleep enough, but there's certainly something going on in that active little brain of his as he drops off!