The Mongols bred their horses for endurance. If you have ever read anything about Ghengis Khan and his exploits (GK is my true hero) there were some bits about arabians and Chinese bred horses that did not stand up to the rigors of the movement of his troops. Maybe these are more modern say around 1200 or so, left over from the Reign of Ghengis Khan.
The Tibetans were horseback warriors too at one time. A pre-Buddhist king conquered nearly as much territory as Genghis Khan did. As far south as Delhi, north to Mongolia, as far east as Beijing and he started moving west through what is now Afghanistan scaring the crud out of the Muslims. He was a lot like Khan in his methods too. Once the opposing force surrendered the men were all welcomed into his army and the people were protected, as his subjects, from reprisal, looting, raping and so forth.