The bottom line would seem to be the State Fair does not own the land and has no legal authority to ban guns on property it leases.
Ken Paxton
Texas State Fair Starts Today, AG Still Appealing Gun Ban
Texas Attorney General Ken Paxton filed an appeal with the Texas Supreme Court in a case challenging a lower court ruling that the State Fair of Texas could ban firearms during the event.
Texas Attorney General Sues Dallas Over Gun Free Zones at the State Fair
Texas Attorney General Ken Paxton filed a lawsuit against the City of Dallas and the State Fair of Texas for banning firearms from the State Fair.
TX: AG Paxton Directs City of Dallas to End Gun Ban at State Fair
Texas State Attorney General Ken Paxton sent a letter to the city, directing it to end this policy, which violates state law prohibiting restrictions on the carrying of firearms on property owned or leased by a governmental entity
Texas Leads Multi-State Legal Challenge Against Biden Administration Over Firearm Regulations ~ VIDEO
The legal challenge targets what Paxton describes as an “unlawful ban” on private firearms sales imposed by the Bureau of Alcohol, Tobacco, Firearms and Explosives (ATF).