The stables structure is the only way to obtain horses or mules in Civ-War. A "Horses" Trade Good that is socketed into your town is required to buy horses. However, you can still buy mules even without the "Horses" Trade Good.
You can use this structure to teleport to any other town with a stables in a radius of 180 chunks (2,880 blocks). But it is not always like this. Some conditions will cause you to travel not as far.