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Id assume a horse thats unlocked or has the potential to unlock the fountain feature in the grand prix, or a horse that has the black market item "water of youth". If this isnt the answers your looking for ask in the gameplay forum and add more details

the only other thing I can think of is they mean "foundation" horse. which is a horse who's parents are Ouranos and Gaia. the horses you get when you first start out, that you get from promos.

A fountain horse is not a known term on Howrse so I think the topic starter indeed meant a foundation horse or foundie in short.
See the other answer for more details.