Get. Everything. In. Writing.
I cannot stress this enough for BOTH sides of the agreement.
Basic things like who supplies the tack. Who pays for the board, vet, farrier. Who does the worming, shots. How often can the leasing party ride. Time of lease? (month to month or for x period)
More intricate details -
Does leasing party need to take lessons? If yes, with who and how often.
Can horse leave property?
Can leasing party have friends/family/other boarders ride the horse?
Is horse for sale? Does leasing party have first right of refusal?
Here's a kicker we've had to add to ours -
NO cutting of mane or tail. Yep TWO different leasing parties on two different horses cut the mane and tail. Both Arabs and both got the page boy cut. So sad.
Ask about less than favorable habits.
Does horse - bite, kick? Paw or pull while tied. Buck or kick out under saddle?
ANYTHING you can think of to ask is not too stupid to put in the lease agreement.