I agree with Skyhuntress. The cost of leasing depends, generally, on three variables. The type of lease (1/4, 1/2, full, free, etc..), where the horse is boarded (board rates ban be anywhere from $150-$1500 a month), and what type of horse you are leasing (schoolmaster, or just a horse that needs exercise).
My family is leasing a horse right now in a "free" lease. Basically the owners have sent us the horse, in trust that it will be well taken care of, and have allowed us to board him where we like, and we pay for all upkeep as if he was our own horse. Signing legal documents and show forms are the only things we really need the owner for.
We have also had experiences with 1/2 leases. Generally people who will 1/2 lease out their horse just want someone to come and exercise it, so there is no fee involved with the owner, just half the board and upkeep expenses (vet, farrier, etc..) good luck!