It's also worth noting this isn't a whole USA thing. A number of states, like Massachusetts where I live have banned open carry. I imagine people do bring them to zoos in open carry states, but I've never seen a gun be brought into a zoo in Massachusetts (or anywhere, for that matter).
I do remember though when I went to Cleveland Zoo there was a sign outside the entrance stating that based on Ohio state law, they were required to allow firearms outside, in bathrooms, and in shelters. They were banned in all the animal buildings though.