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If she received the horse as a gift, then the horse belongs to you, even if you have been sharing costs on maintenance. You would, since you have been paying expenses, be entitled to sue her to recover all of your money you spent caring for her horse since she turned 18. Since it is her horse, it is her legal responsibility to make payments. If you present her the proof of your payments and make a demand for payment and she refuses, you can sue her in court for contribution as it is her horse solely as it was a gift to her.
The only defense she would have is that as there was no written agreement between the two of you, she would claim your payments were gratuitous or a gift to her and you would have to prove that they were not a gift and she was supposed to pay her share at least of the expenses.
I am afraid that your only recourse though if she refuses to pay when you ask would be you do have to sue her to seek to recover the money you have paid for caring for her property.
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