Since the HOA docs were not supplied to you and they are a material part of the trransaction you need to speak with a real estate attorney to see what can be done.
Sorry to hear of your situation but I agree with the agent below that you will need the advice of an attorney. Perhaps you could obtain a special permit for the animals. I would see if there is some kind of a loophole as I am an animal lover also.
Good Luck and let us know how it works out.