Month-to-month rental of horse-stall.
As a general rule, a tenant is not required to occupy the rented property (known in law as a leasehold). A rental by the month is generally referred to as a month-to-month tenancy. Many tenants remove themselves and/or their property from the leasehold prior to the termination of the tenancy. You as a tenant would as a general proposition of law be able lawfully to remove your property--your horse--from the landlord's barn on any date in the month of July 2009 or thereafter.
Also as a general rule, a tenant's notice of termination is effective when received by the landlord; however, many states have a rule that a letter is received by the recipient so-many days after being mailed, but the delivering party must be able to prove that the letter was mailed on a certain day. Upon the facts you have stated, the only difference of opinion between you and your landlord is the termination date. Many states have statutes that authorize attorney fees in small-claim cases. The attorney fees to collect 10-days rent could be greater than the pro-rata rent. In any event, the pro-rata rent could be paid or not in August 2009.
A way to build better relations with your landlord would be to give your landlord immediate notice upon moving your horse, thereby allowing the landlord the opportunity to rent the stall to another person. Also, and again as a general rule of contract law, a landlord must mitigate damages. That means that a landlord with a vacant leasehold may not simply allow the leasehold to sit vacant, but must immediately attempt to find a new tenant for the leasehold.
Please read the relevant information that appears in the linked websites.