Horses do need about 2 hours of REM sleep in 24 hours but it doesn’t have to be 2 hours consecutive, plus they can miss a day or two.
For REM they need to either be lying down sternal with their nose on the ground or else flat out.
If they can’t lie down at all to for many days due to bad footing or bad hocks or stifles, they can get wierd narcolepsy things happening.
At our barn the horses can all see each other in the runouts and they definitely sleep in shifts. My mare sleeps typically after her breakfast hay drops. If I drop by the barn at 11 pm several specific horses are always out cold flat but my mare is wide awake and ready to party. Other horses reliably sleep in the afternoon despite all the coming and going of people and horses.
If my mare is sleeping at an unusual time its generally because of some disruption to her day like there was loud construction work in the morning.
Her bright hello! look when I arrive even if she doesn’t jump to her feet is very different from her dramatic look of pure misery when she drops for colic.