Most state fairs are held on private property. Many have official state recognition, but most are funded without state assistance. Even if the land they are held on is owned by the state, they still have a private permit, if not lease, for their activities, and no, you do have first amendment rights to do whatever you want to on such property. Your conduct has to be proper for the purpose of the property. Certain public lands, such as town squares, are fit for noisy greivances. But a school is public property, but you can’t just go screaming down the hallways. A road is public property, but you can’t just lean your hand on the horn as you circle the block over and over again.
What is the source for your information?