Caroll (the owner of the foundation) always has a selection of foals from each breed (except the wild breeds) available to choose from. There will always be 4 horses of each breed (so they will automaticly replaced when you take one horse with a new one). They cost 5000 HRC and 1 Foundation Ticket (FT) each.
On each continent, there are 10 mares and 10 stallions per breed which get paired at random to produce the foundation foals for that breed on that continent. Traveling can pay off, as each continent has its own foundation stock and, as a consequence, different bloodlines. If you travel by plane, you will be able to see the available foundation foals for whatever continent you're currently on. Should you buy a foal from a continent that is not the same as your home continent, a transportation fee of 500 HRC will be added to the usual price, totaling in 1 FT + 5500 HRC. Then the foal will automatically appear in your stables at home.
You can check the horses stats by clicking on the horse if you want to see if you like it. If you want to buy the horse you click on the button under the horse.