Interesting. I know Tawakoni State Park has a ban on all firearms.
Q: May I carry my gun into a state park when I am traveling?
A: Our rules state that you may not show/display or fire your gun in a state park. If you have a valid Concealed Handgun License, you may carry your handgun in many state parks. But even with a CHL, handguns are not allowed in parks that are leased from the federal government. Check with the park before you go. Refer to Texas State Park Regulations for specific regulations - 59.134(d).
Tawakoni State Park is leased from Sabine River Authority and is an agency of the state. It cannot ban CHL.
MOST parks, city/county/State/ are posted with "NO FIREARMS" signs ... like most grocery stores, liquer stores/restaurants/Convenience stores/Walgreens have the "unlicensed carry prohibited signs" ... those don't apply to licensees carrying the type of handgun licensed to carry .... however, a CHL doesn't mean you may carry a rifle/shotgun/long gun into a no firearms posted park..