Texas Hunting Questions

I have learned that I will be going to Texas in the end of October for two weeks for work and what better way to spend my down time than to hunt with airguns. I have been doing some research on places I can hunt and what I can use to hunt. On the TPWD website, they show several public hunting and game leased areas in the Dallas Ft. Worth area, but most of them say shotgun only with lead free ammo. My question is if I go to one of these public hunting or game leased areas, will I be legal to hunt with my airgun? Also, the TPWD site says airguns are only legal to hunt squirrels with. It doesn't state whether that's in the public hunting or game leased areas. I know I've seen on youtube some big named airgun hunters harvesting other animals with airguns. Any information will be greatly appreciated on where and what I can hunt with airguns.
 
Pigs, Coyotes, Squirrels, Eurasian Dove, Grackles, Cotton Tail Rabbits, Jackrabbits, Turtles. I hunt all but squirrel because they don't range where I live, however since I am a land owner I don't even need a hunting license to dispatch "pest" animals which is what my list above comprises. Personally I would call TPWD and ask them about hunting on public land of which there is very little in Texas. I believe the video's you refer to are probably in Arizona which is "airgun friendly" on most game species.

Thurmond
 
I've talked to a TPWD officer and he said that i could hunt any non Game animal with an air rifle. So if you have to have a hunting license for it such as Whitetail deer, Turkey, white wing dove, etc. then you have to use a center fire rifle. But hogs, rabbits, pigeons, squirrels etc (just as Thurmond said) can be taken with an air rifle.

I have a place that you can come shoot on but if you are going to be in the DFW area you will be about 5 hours away.
 
Thank you all for your help. It sounds like I need to make some friends with private land when I get to Texas :) If I don't, I'll be happy wondering the public land in search of squirrels that I probably won't see. It's nice to just get out an walk through nature. I was in Tucson for work not too long ago and I roamed the desert for two days straight. I got one shot at a jack, but I was happy to be away from the real world for a bit.