What is it called where a horse sleeps?

Most horses will sleep standing up, however, not all, so if they are in the wild, they may sleep on grass or the bare soil to sleep. If however the horse is domesticated and it sleeps lying down, then it's up to the owner what the horse sleeps on. this can include grass or sand in a paddock or field, or bedding in a stall which can be one of many materials including but not limited to: Straw, Pine Shavings, Pine pellets, shredded paper, paper pellets, hemp, flax, straw pellets and other materials.

Keep in mind that all horses must lay down at some point to get REM sleep or they will not have gotten enough deep sleep, no matter if they are wild or not. Horses more or less 'nap' standing up.