As for livery you'll have to debate feeding, turnout, exercise, cleaning of stables etc

If it's a loan you'll need to draw up a list of rules etc such as who pays bills, whether or not a certain discipline is prohibited, what happens should the horse be injured and permanently damaged i.e. Reimbursement or a horse of similar calibre... who gets position of passport or photocopy, length of loan or length of time to give notice of termination...