With that wording i would say YES you would be within the bounds of the law to open carry, weather you get arrested or not I don't know. I am sure it would NOT hold up in court if they arrested you. One thing in question though is weather or not the zoo was built with any gov. money cause you might not be able to go in any of the buildings. I would love to see someone open carry'ing in a place where they put a "no concealed sign" out front but I feel sorry for that person because the police will probably try to put a felony on you and the time spent in jail does not sound tempting.
That being said I personally would not do it because of the potential negative outcome. However if you must do it yourself I would love to go with you and take a video camera, since its at zoo won't look out of place, and video tape the sign going in and then if you get confronted by anyone or mabey the police get it all on tape that way we might have a case. Also get you on tape quoting a few ohio statutes to the officer.
WELL you could also say that the gun is for your own protection in case of a big animal getting loose and attacking you.