What Speed said ^^^^.
There's also something called a mechanic's lein, which allows you to take possession of property left in your care when the owner of the property owes you money. Named because it originally was written for mechanics, giving them a lein against a car title when they were owed money for repairs.
However, I'm not sure if you can file one with the court in the absence of an actual board contract.
You could try calling the clerk of the court in your county and ask about the requirements for filing a mechanic's lein to start off with; but I suspect you will need to talk to an attorney to get clear title to the horse.
He looks great in your photos, good job. BTW, it's great that you have those photos as documentation of the care you've provided - that will help your case.