Introduced in the experimental version of Rust, horses are passive animals that will not attack the player. They will not attack you if you shoot at or otherwise threaten the poor beast. It will simply flee for its life, running at speeds much faster than your two legs could ever hope to reach. After running for about thirty seconds, the horse will tire out and will either stop completely or slow down to a leisure walking speed.
At the moment, horses come in only a dark-brown color, in line with the main colors of the game. Horses may also bare a darker-brown/black mane and tail. It is important to note that currently, horses are not a mountable animal. However, the developers have stated that horses will become rideable in a future update. In fact, one of the developers has posted a video to Facepunch.com, a popular forum for the game, showcasing animations. Some animations include galloping, trotting, walking, sleeping, idling, and a courbette (where the horse balances on its hind legs before jumping).
When killed, horses may drop cloth, raw wolf meat (placeholder), bone fragments, and animal fat. Taking down this animal will not be easy with melee weapons, as it will most likely evade your hits before you deal critical damage. For that reason, it is highly recommended to use a ranged weapon such as a gun, hunting bow, or crossbow to kill this majestic animal.
Video Credit: Minh Le