I think it was back in the late 1800's when the state surveyor said "All the land in Texas is gone!" There is no "open range". The only places you can achieve what you are looking for is in the Big Bend area as previously noted or one of the natural Forest preserves in east Texas. One thing to always keep in mind is to know who's land you are on. Rural land owners sometimes can be less than hospitable.
http://www.nps.gov/bith/
http://www.fs.fed.us/r8/texas/
http://www.tpwd.state.tx.us/spdest/f..._bend_country/
Enjoy your time outdoor's, but respect the rights of private land owners. Many areas of the national forest can be entered with out fees. However it is always wise to let the officials know where you intend to go and time of return. The above sites should prove useful to you.