Small claims is different from county court in a couple different ways. The main differences in small claims have to do with discovery procedures (how you request information from the other party) and the court automatically assigning you a court date. I've attached the rules for both small claims courts and general civil procedure.
As the other contributors have stated, the first step toward seeing what your options are is to review the lease agreement. It would be wise to contact a landlord/tenant attorney who can take a look at it, sooner rather than later, considering the lease kicked in on November 1st. Best of luck!
The answer to your question may be found in the HOAs covenants. Many times an HOA will require that the property owner get the HOA's approval before the tenant can move in. If the property owners fails to get HOA approval before the tenant moves, then they may have grounds.