My usual preface here...I ain't not no lawyer, and if I need real legal advice, I finds me one and pays for it.
However...that doesn't mean I don't have a brain that I can use to at least question things. (Then I can make best use of my dollars when I seek that legal advice.)
"In order to leave the community by foot, bicycle, or motor vehicle I must pass through the aforementioned common areas."
This statement itself begs legal clarification. While an HOA can lay down lots of bylaws, enforceable in the courts, within your actual domicile itself is another matter. This is not to say that they have absolutely no authority over anything at all within the domicile, but rather their authority is more limited...and, of course, has to be explicitly spelled out.
An HOA cannot abrogate your legal rights you hold as a citizen. For example, if the police came to your home and wanted to conduct a warrantless search, and you denied them permission to do so, the HOA cannot step in and grant them that permission simply because they may have some authority themselves to enter your home under specific conditions outlined in the HOA agreement.
Let's look at another circumstance involving firearms restrictions. Keep in mind, however, that what I'm about to discuss deals with actual statutes (law) and not a civil contract (like an HOA). There are very real differences between the two and not everything applies (directly or indirectly) from one to the other. However, both have a lot to do with the right to keep and bear arms itself.
The Gun Free School Zone Act (GFSZA) of 1990 clearly states within it the following:
It shall be unlawful for any individual knowingly to possess a firearm that has moved in or that otherwise affects interstate or foreign commerce at a place that the individual knows, or has reasonable cause to believe, is a school zone.
It also defines school as "a school which provides elementary or secondary education, as determined under State law" and a school zone as "in, or on the grounds of, a public, parochial or private school; or within a distance of 1,000 feet from the grounds of a public, parochial or private school".
Anybody with an ounce of brains can pull out a map of any city/town and start drawing the 1,000 foot line around all the schools/school properties and see that this includes a rather significant portion of the city/town...and that a great many private properties are included.
Therefore, the GFSZA also includes a number of exceptions because they cannot outright deny any person their RKBA simply because their private property lies within the defined school zone. I won't list them all, but I will cite a few. Such as on private property not part of school grounds. Or unloaded an in a locked container, or locked firearms rack that is on a motor vehicle.
These are legal exceptions within the statute (i.e. "laws"). These things to not automatically cross over to civil contracts directly. However, there are several legal foundations that statutes and civil contracts are based upon which dictate how these statutes and contracts may or may not be written.
State laws also allow for the lawful possession of firearms within your own home, whether you own that home or are renting it. And that includes hotels (At least if your state has statutes to this effect. SC does under their Protection of Persons and Property Act, SC Code 16-11-410 through 450.)
Being a member of an HOA does not mean the HOA can forbid a person from possessing firearms within their own home. Nor can the HOA affect rules which prevent a person from transporting their lawfully owned firearms to and from their own home.
This would mean that while an HOA MAY have rules which do not allow firearms in certain common areas, they cannot completely surround a person's private property/home with "common areas" and use that to prevent transportation of legally owned firearms to and from the person's home. You may not be able to "carry" a firearm in those common areas, but you MAY be able to "transport" a firearm through them.
HOAs may be very restrictive indeed. But they do have limitations. In my non-legally educated opinion, this is one of them for the reasons I outlined above. HOWEVER...find yourself an actual attorney who practices law in your jurisdiction and pay him for that hour or three it would take to get his professional opinion on the matter.