I believe I have the final version of the thing.

A level 1 player can have one horse
A level 10 player can have 10 horses

If you wish to have more horses, you would have to purchase a license from a License Shop (that will be built soon)
The license does not come cheap:
For 10 extra horses you have to pay 50000 coins
For 10 more, you would pay another 100000 coins
For 10 more it would cost another 200000 coins.