Leasing is VERY common, I doubt you'd have too much trouble. The only real problem I see is usually leases come up in the fall and end before summer, because a lot of college kids lease out their horse while they're away at school. They come home to ride in the summer.
But you still can find a lease. Also, many leases are month to month, not all sign a year contract.
I would go on either dreamhorse.com or horsetopia.com, or equine.com
I know dreamhorse has a wanted section, I think the others do too.
Post an ad that you're looking for a LEASE (give a breif description of the type of lease you want -- free lease, partial, full, etc) and the period of time in which you would want to lease.
Also, search those sites for horses that are for lease, you can specify for LEASE under the Advanced Search option.
Even if an ad isn't QUITE perfect but is close, talk to them anyway. As I have leased out horses before, I was always willing to bend a little on the terms.
"The white horse moved like a dancer, which is not surprising: a horse is a beautiful animal, but it is perhaps most remarkable because it moves as if it always hears music."