I thought in the past open carry was not allowed in state parks, even after unlicensed carry became legal elsewhere. I even saw a guy open carrying in a state park get stopped and talked to by TPWD LEO, and I thought they ticketed him. Reading the rules now that no longer seems to be illegal.
https://texreg.sos.state.tx.us/public/readtac$ext.TacPage?sl=R&app=9&p_dir=&p_rloc=&p_tloc=&p_ploc=&pg=1&p_tac=&ti=31&pt=2&ch=59&rl=134"(d) Arms and Firearms. It is an offense for any person to display or discharge an arm or firearm in a state park, except while:
(1) the person is participating in a public hunting activity within the state park as authorized by applicable public hunting rules and regulations;
(2) the person is fishing by means of lawful archery equipment or is participating in an authorized, supervised recreational or educational activity;
(3) the person is licensed to possess and carry a handgun under Government Code, Chapter 411, Subchapter H, and is in possession of and carrying the handgun in compliance with applicable law, including, but not limited to, applicable regulations adopted pursuant to Government Code, Chapter 411, Subchapter H;
(4) the person carries a handgun in a holster in compliance with Penal Code, Chapter 46; or
(5) the person has been authorized to do so by written order of the director."