Now you've got me, as I'm not up on all the rules & regs TPWD has in place regarding hunting. They have an extensive
hunting information section on their site that contains a wealth of details. Hopefully, the content there can help clear some of the fog surrounding the various hunting options and regulations in place.
I do know some of the more popular places and/or times of year to hunt have "lotteries" where registered hunters have to vie for the opportunity to participate in certain hunts, but this is not the case at every park nor for the entire duration of the hunting season, I don't believe. Also, I don't
think you're limited to only per-location hunting licenses, as that could get expensive in short order!
One thing to consider is the rules regarding hunting in Texas State Parks may differ from the rules applied to hunting in Texas' Wildlife Management Areas (WMAs) such as Walter E. Buck. WMAs tend to have more opportunities for hunters, since wildlife management (and that includes culling the herd through public hunts) is their primary objective.