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You are absolutely correct, the university must hold the horse for greater than 3 years for there to be no repercussions to the donor.
If the University were to sell the horse after three years, for as you say 10K, then the donor would have to recapture a portion of thier prior year deduction taken (i.e. declare taxable income).
Note that there are two exceptions but I don't believe that they will apply to horses: see below on page 3: