Write a letter back to the HOA appologising, but explaining your predicament in not being able to get out properly, and that you would like some form of pedestrian gate that members can have a key to, or have some sort of sensor card to get through the car gate (as I assume the cars probably have a card/sensor on them to tell the gate that they live there?).
There's no reason why you and the HOA can't be reasonable about it.
I'm sure they would rather you were able to get in and out safely than having to climb through gates and possibly damage them or hurt yourself.