Have you met the Hermit and noticed that he has some pretty Welsh Ponies standing there? Once you are level 7 and have reached reputation level Friendly with the Hermit, you will be able to buy the ponies that he holds very dear to his heart.
To gain a reputation with the Hermit, you need to do the daily tasks he has for you, and you can also do the two races that start from his cottage. The daily tasks are marked with a blue exclamation mark above the Hermit's head.
When the Hermit feels that you are allowed to buy the ponies, they will be repositioned and have a coin above their heads.