Instructions
Ride your horse to the nearest town. Use the in-game map, which can be accessed from the ̶0;Pause̶1; menu, to check for towns that are close to your current position.
Check for hitching posts in front of the various buildings within the town. You can usually find hitching posts next to saloons, general stores and sheriffs' offices.
Move your horse to the front of a hitching post. Make sure that there are no obstacles between the hitching post and your horse.
Hitch your horse when prompted. Press the ̶0;Square̶1; button for PlayStation 3 or press the ̶0;X̶1; button for Xbox 360. The game will perform an autosave and notify you that the horse is now your "trusty steed."