Can a private homeowner's association for a subdivision legally enforce an HOA rule that says residents...

I am not familiar with South Carolina law. In general, the HOA derives its power from a document which is recorded against all the property which is part of the Association, including the lots or units, along the property owned by the Association as common area. This document goes by different names in different jurisdictions, but it's often called the Declaration, or the Declaration of Covenants, Conditions and Restrictions (CC&Rs) or the Master Deed. I'll refer to it as the Declaration, here. Somewhere in the Declaration is a description of all the property which is subject to the Declaration. This can be a paragraph within the body of the Declaration, or several attached exhibits with legal descriptions, or a series of annexations or amendments which were recorded at different times during the development. If the county streets are not part of the property subject to the Declaration, the Association has no real legal authority over it. However, there are instances where a developer will record a Declaration against a larger piece of property, which is then subdivided into Lots, common area, streets, etc. If this is the case, you may be able to enforce those restrictions on County owned streets. Also, I have seen a few cases where the language was in the Declaration, and the County Courts upheld the Association's right to enforce parking restrictions even though those streets were not part of the property described in the Declaration, ruling that it's part of a common scheme to maintain property values, and that owners were aware of the rules by virtue of the recorded Declaration when they bought their property. So, bottom line, the answer is that you should check with a local attorney. I hope this helps

If that was in the HOA rules before you purchased your home, then yes, they can enforce that rule. That may be a public street but, it may have been part of the agreement the builder signed with the zoning commission. Residents would not park on city streets but use their own property for parking, leaving the city street for use by the general public. You could be given a ticket by the police & subject to a warning by the owner of the property from whom you bought your home.

I don't think a car could be towed for it unless there was a no parking sign on the street or the curb was painted yellow. Some associations even dictate the color palettes you can use on your home, but I don't think there are any legally binding laws against another color.

I don't know about S. C. but I live in Tucson, AZ and I can show you several neighborhoods just like that. So I guess it is legal here, anyway.

You can bet that it is not legal as it is a public street.