When you start you have 2 slots for horses.
The second box is free but to get more room for horses you need to upgrade.
Box 3 requires
*4500 horse bucks
*4 Paint
*5 Planks
*4 Plaster
*1 stable hand (meaning a friend added to your account)
Box 4 requires
*6000 horse bucks
*5 Paint
*5 Planks
*5 Plaster
*1 Stable hand
and so on...
Note: You actually start with a lot of free things unlike other games when it comes to the materials needed you actually start with almost 20 of everything. You really only need to work on making money to get most of the things you need to complete buildings and expand.
As for buying more horses, there will be quests that tell you to do so. In the beginning you might be upset that you can only buy one horse without facebook cash as you can see below in the picture of my level 1 shop.
As you level the horses that required facebook cash become available for horsebucks as seen in my level 15 shop.
