I am also new to hunting, but not new to fire arms in Texas.
When my son and I decided to get into hunting I studied the non game and exotic hunting information, it stated that hogs can be taken by any legal means. It did not specify a difference in legal means between privet property or public property. As far As I can tell legal means are the same no matter if you are on public property or privet property.
Please remember that many public hunting areas have there own rules so check before you go.
I spent my lunch time looking for that statement in the Texas Outdoor Annual online and could not find it but Here are some links to the information I did find.
As stxranchman stated, good idea to talk to Texas Parks and Wild life or Game Warden directly.http://tpwd.texas.gov/regulations/outdoor-annual/hunting/general-regulations/means-and-methodshttp://tpwd.texas.gov/huntwild/wild/nuisance/feral_hogs/