I was there in the spring. Not sure on the Ohio laws but pretty sure I remember no gun signs at the Zoo. I wouldn't be seen in that neighborhood without one.
The Cincy zoo is kind of an oddity. The parking lots are privately owned and you will see signs posted. However the zoo itself is publicly funded and therefore cannot forbid carry - there are no signs in the zoo itself. Personally I ignore the parking lot signs.
Went today saw no signs posted about weapons in the parking lot or at the gate. I doubt with cold weather clothing anyone noticed my M&P 45C on my side.
When we were there last year I remember seeing a sign when entering the parking lot. I did not see a sign when entering the zoo itself. Signs carry weight of law in Ohio. The gun was locked in the vehicle safe because the hotel we stayed at (Great Wolf Lodge) had signs at every entrance.
We parked in the back parking lot instead of the main one. There was a lot of construction, maybe the signs were removed for that, either way there were no signs that I could find.