Steve,
As for assigning parking spaces, it depends on the development. I live in a Town Home development (HOA not COA) and the parking area/roads are considered common area (and specified as such within the CC&Rs). The Board assigned two spaces per lot with the extras (which aren't many) being used on a first come first served basis.
Mike,
VA law,
§ 55-513, specifies that [emphasis added]:
The board of directors shall also have the power, to the extent the declaration or rules and regulations duly adopted pursuant thereto expressly so provide, to (i) suspend a member's right to use facilities or services, including utility services, provided directly through the association for nonpayment of assessments which are more than 60 days past due,
to the extent that access to the lot through the common areas is not precluded and provided that such suspension shall not endanger the health, safety, or property of any owner, tenant, or occupant and (ii) assess charges against any member for any violation of the declaration or rules and regulations for which the member or his family members, tenants, guests, or other invitees are responsible.
Based on this statute, I'm surprised that your Association may prohibit the use of the parking area as that could prohibit access to the lot and an argument could be made that having to leave a vehicle (normally allowed to park within the complex) on the road can endanger the vehicle (property) as it's more likely to be broken into than one parked on the common area.
Tim