This could be done on the third island when usually appear some newer rides.
The basics are your regular horse, the alpha male deer and here there is a chance to see a battle horse and also the "Percheron" horse.
To unlock use them save the diamonds and then the right number of coins (usually 3).
If you manage to ride all four variants you will unlock it.
There are more creatures to ride on the game but they are unlocked later (and I don't want to spoil them)