Without going there to see if it is posted against CC, the NC Zoo is a no-go for OC. Admission is not free, so OC is not permitted.
http://www.ncga.state.nc.us/EnactedLegislation/Statutes/HTML/BySection/Chapter_14/GS_14-269.3.html
§ 14-269.3. Carrying weapons into assemblies and establishments where alcoholic beverages are sold and consumed.
(a)
It shall be unlawful for any person to carry any gun, rifle, or pistol into any assembly where a fee has been charged for admission thereto, or into any establishment in which alcoholic beverages are sold and consumed. Any person violating the provisions of this section shall be guilty of a Class 1 misdemeanor.
(b) This section shall not apply to any of the following:
(5) A person carrying a handgun if the person has a valid concealed handgun permit issued in accordance with Article 54B of this Chapter, has a concealed handgun permit considered valid under G.S. 14-415.24, or is exempt from obtaining a permit pursuant to G.S. 14-415.25. This subdivision shall not be construed to permit a person to carry a handgun on any premises where the person in legal possession or control of the premises has posted a conspicuous notice prohibiting the carrying of a concealed handgun on the premises in accordance with G.S. 14-415.11(c).