... is good in the states you mentioned.
handgunlaw.us is a website you might want to check out.
http://handgunlaw.us/
This link has info on Texas's gun laws, and a map at the top showing the states that recognize a Texas permit. OK, AR, and LA are all in blue, which is good.
http://handgunlaw.us/states/texas.pdf
You'll want to go to the main page, to access the laws for those states, so you can see what their prohibited areas are, and what other rules you may have to follow when you visit them.