Here's some digital wisdom (you probably don't want) from a guy who owns a W.W.II airfield and a "warbird" Navion that he's flown to air shows in Southern California.
Warbirds: First off let me say folks are very emotional about these planes. Warbirds were built by the American public, for the American public to defeat evil and preserve our way of life. It's sometimes difficult for folks to think they are privately owned being such a national symbol. They are something people can understand. I've never at an air show had a guy ask me what I do. Not once. The questions are always directed at how if
he flew the plane how would he do it. I realized I (owner pilot) was an accessory to the plane. Secondly people don't know the plane isn't public. They paid for the show, so don't we get to touch the plane? I once at a show had a family of five climb up on the wing and take pictures when I stepped away.
Airfield: I have had several large events at VAF - Vosburgh Airfield (5CN4) and have some conclusions. First off - the general public can be real jerks and at times extraordinary stupid. I don't know how else to put it. At events people get emotional, people get silly, people get animated and sometimes don't think. (Not to mention the effects of alcohol.

) As the hosting airport you are responsible. Event insurance is very expensive - guess why! 98 percent of people are great, the other 2 percent can litigate you out of your home.
So in short: Are you willing to take the risk and deal with the stress to allow the public to enjoy / use your property?
Best,
Jason