JMHO
Blacks Law Dictionary defines the term "Shelter" as "A general term used in statutes that relates to the provision of food, clothing, and housing for specified individuals; a home with a proper environment that affords protection from the weather."
With that said, the so called grandstands would be classified as an "open air arena" not a shelter. The problem is, does the open air arena have a class "D" liquor permit. See 2923.121 and 2923.126.
If no liquor permit open carry would be legal. One caveat, cops for the most part don't know this.
But, if a class "D" permit is issued you would be in untested waters.
Open carry in the fair buildings are legally permissible.
On May 1, 2012 the attorney for Vandalia, Ohio (Gerald McDonald) issued a letter to police chief Douglas Knight discussing issues relating to the open carrying and the concealed carrying of handguns. As to open carry attorney McDonald stated in part:
OPEN CARRY
For the most part the above law is specific to concealed carry, In other words, while a person may be prohibited from carrying a concealed weapon in a public building under 2923.126(B)(9), he would not necessarily be prohibited from having an open weapon in a public building. However, some sections of Chapter 2923 apply to open carry as well as concealed carry weapons, For example, R.C. 2923.126(C) allows private employers and landowner to prohibit persons "from carrying firearms or concealed firearms" on private land by posting a sign. (Subject to certain exceptions.) likewise, 2923.123 makes it illegal to have a firearm in a courthouse. or in another building or structure in which a courtroom is located. (Based on this, it appears that one cannot carry a firearm, either concealed or open, into the Vandalia Justice Center)
This is why the ORC only points to five places that carrying open or concealed is prohibited. Those are a jail, courthouse or used as a courthouse, school, state run mental hospital and bars (unless you have a CCW).