If it's designed to be used in a minigame, you could try searching the owner's brick-group for the first brick, then set its spawnbrick to that and any other necessary variables. (look at a horse spawned normally) This might fail if they end up deleting that brick, though.
Next time you might want to give that information in the first post instead of me having to guess as it turns out to be very relevant to the question you're asking...
I'm sorry. The horse is spawned "on" a brick, but is actually spawned then moved with a setTransform. This is because when the horse is killed, it's supposed to "respawn" on a random spawn within the simset. This makes it difficult to give it a set spawn, though I suppose it's possible. Could you tell me the variables for the spawn and ownership, or are they $[number].spawn and $[number].owner?