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:

Increase in horse trainability provided by each saddle type:

Saddle Type
Level 1:  Regular

Level 2: GreatLevel 3: SuperiorLevel 4: ClassicLevel 5: GrandLevel 6: Pristine
Star Saddle 7% 14%    
Heart Saddle 7% 14%    
Polkadot saddle 5% 10%    
Checkered saddle 5% 10%    
Diamond saddle 5% 10%    
Horizontal Stripe saddle 3% 6%    
Vertical Stripe saddle 3% 6%    

Saddles Levels 3-6 are currently not available, with the exception of the Hardcore Saddle which is a Level 6 "Pristine" item.  

Other Saddles

Level 1: Regular Flame Saddle 

+ 3 Strength -1 endurance 

Level 1: Regular Ice Saddle 

+3 endurance -1 strength 

Where can I buy saddles?

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.