It's not about National Forests. It's about Texas hunting laws.
http://www.tpwd.state.tx.us/publicat...al/hunt/means/
From that website is this:
"Firearms
Game animals and game birds may be hunted with any legal firearm, EXCEPT:
white-tailed deer, mule deer, desert bighorn sheep, and pronghorn antelope may NOT be hunted with rimfire ammunition of any caliber.
shotguns are the only legal firearm that may be used to hunt Eastern turkey during the spring Eastern turkey season (see County Listing). Rifles and handguns may not be used to hunt Eastern turkey.
pellet guns and other air guns are NOT LEGAL.
fully automatic firearms are NOT LEGAL.
firearms equipped with silencers or sound-suppressing devices are NOT LEGAL.
a shotgun is the only legal firearm for hunting migratory game birds (see Definitions - Legal Shotgun).
Nongame Animals (Non-Protected): Any lawful firearm, pellet gun, or other air gun is legal."