I just went to the SC State Fair website and reviewd their "rules and regulations". Predictable, "no concealeable weapons".
I've never be able to determine if the SC state fairgrounds are actually a municipally-owned property or privately owned.
If they are municipally-owned then they cannot legally make you disarm...the only parts off limits are the municipally-owned buildings themselves.
If the grounds are privately owned then they're supposed to use state compliant signage at every entrance. Last time I checked, there were signs on the windows at the ticket booths but they were not state compliant (this has been several years ago.
Even if the grounds are privately owned and not posted in accordance with state law you can still be notified by the owner's legal representative (in this case, the cops working the gates) that CCW is not allowed once it has been determined that you are carrying. In this case they are giving you notice and you'd either have to leave (and disarm to come in) or face arrest for trespassing after notice if you refused to leave. I don't believe that they could legally arrest you for carrying simply because the fair mgt. says no weapons (providing the grounds have no state compliant signage.
I'm out of breath....