I am not a proponent of HOA's but we live in one with deed restrictions. I somehow have gotten onto the board and have found myself as the sole remaining board member due to attrition. I have researched the hell out of it and talked to a lot of real estate lawyer buddies and gotten scared enough to take advantage of some retained attorneys our management company pays for.
What I have learned is that if they are deed based, and have any form of community property, do not eff with them. Sure you could go into litigation but as much as you would think they do not want to go there or pay for it, they are typically heavily over-insured and those *******s get off on it. So they slap you with a fine, then a lien, then collection charges, then legal charges, $#!+ gets out of hand quickly. My advice would be to kiss whoever's ass you need to in order to get your arbor approved. If you can't then there is likely some basis in the CC&R's that they are using. If that is the case, you will need to figure it out.
Now some will say "they cannot foreclose" not true, they can foreclose, they have to remove any superior liens in order to do so. If you piss them off bad enough they can and might do it. Sure you will get your due process in court, but plead your case to yourself and decide what a judge would rule. Remember you agreed to the HOA when you purchased. You have benefited in quality of life and property appreciation. You bypassed the Arch review committee, you built your arbor out of compliance, you stuck your middle finger up when they challenged you. OK so you are not going to move, and they are not going to foreclose. You still have a lien on your house that will be dealt with the next time you touch your mortgage.
What you run into with these as some posters have mentioned is consistency. I guarantee the HOA has talked to an attorney, and he has informed them that they must stay consistent to avoid setting bad precedents and the appearance of any of the -ism's. Ignore your lack of permission or architectural style and they have set precedent.
A good plan violently executed now is better than a perfect plan executed next week.
-George S Patton