The Mamluks were able to prevail at the Battle of Ain Jalut due to a better knowledge of the land, better tactics, secret alliances with the Christians that the Mongols didn't know . The Mamluks used their horses to performe quicker maneuvers in the course of the battle and their horses also used horseshoes.
The advantage that the Mamluk horses have over the Mongol horses was that the Mamluk horses had horseshoes, while the Mongol horses did not have horse shoes. In reality the Mongols had numerous number of horses and it was next to impossible to provide all the horses with horse shoes. It was a disadvantage, but they had no other option.
