This has been discussed quite a bit on other forums in Ohio and across the U.S. for that matter. Obviously, these dams are often located inside/next to a state park, national forest, etc. where carry is legal outside of buildings. You could attempt to look up actual boundary lines via the computer, but I for one have found little useful information, and at that it was somewhat conflicted depending on who printed the map. In other words, nobody has (best of my knowledge) ever figured out a solid answer.
But, it's not like there's such a thing as a CoE Police Department, mostly they depend on the FBI or U.S. Marshals for any enforcement duties. Can't remember ever seeing field offices for either of those groups out in the parks, by the lakes, you know?
My advice--worth at least what you paid for it--would be to stay off the dam structure while armed. Do have a current fishing license when fishing, make sure your state issued boat license is current, etc. LE of the state and county level are still encountered in the parks from time to time.
Congress has had bills to address this issue on the table for years now, but none ever seem to make it to a floor vote.
"I have decided not to vote, speak in public, assemble in groups or petition my government either directly or by writing to the newspapers.
Some ignorant person may become alarmed, and we can't have that.''