Each horse has a 'trainability' factor in its DNA which differs from horse to horse.
Trainability is the factor which contributes to a better result (i.e. greater strength or endurance increase) when your horse is trained. Saddles can increase a horse's trainability by the following factors:
Saddles Levels 3-6 are currently not available, with the exception of the Hardcore Saddle which is a Level 6 "Pristine" item.
Level 1: Regular Flame Saddle
Saddles will rotate in the shop on a daily basis. Level 2 saddles will only appear occasionally so be sure to stock up when you see them.