Why and in what ways do horses sleep standing up?

Staying on their feet while sleeping allows creatures to stay on their feet by the anatomy of the supporting apparatus, that is, the tendons and ligaments that stabilize the joints. In essence, these fasciae act like tension bands and allow the animal to remain in a standing position without severe muscular strain.

An adult horse can sleep for long periods of time in the slow or deep phase of sleep while standing, but still needs to lie down for full recovery.