Well I didn't intend to leave the OP in suspense, sorry. But since he didn't specify which car show he meant, maybe no harm was done anyhow.
If he was talking about the event at (Duke Energy) Cincinnati Convention Center, here's an answer: It is owned by the city, or at least they consider it a government building. That would definitely put it off limits to licensed concealed carry. Open carry in such places, with exceptions of courts and detention facilities, theoretically is legal, but nobody wants to be the test case, it would seem.
Additionally, since the Convention Center has Ohio Class D premises-consumption liquor licenses, it would be unlawful for carry of any kind to individuals without an Ohio-accepted concealed handgun license, any time alcohol was being served. Which, as you'd expect, is pretty much during all functions held there. (Okay, maybe they don't serve drinks when a national Baptist church convention group rents the place, for example.)
Sorry about the windy explanation but our laws aren't as simple as people like us wish they were. Color of law explains these things better than I do, by the way.