Not everyone has a lease, and that's okay. Texas has public hunting too.
Most of Texas is private land, but there are still real places to hunt that are open to the public. A yearly permit from Texas Parks and Wildlife opens up close to a million acres, drawn hunts give you a shot at special areas, and national forests and Corps of Engineers lakes have hunting too. Every link below goes to an official source, so always check the current rules before you go.
One yearly permit from Texas Parks and Wildlife opens nearly a million acres of walk-in hunting. It covers the areas below. Check each area's rules in the map booklet before you go.
About 16 national wildlife refuges in Texas allow some hunting. Many deer hunts are drawn through TPWD, and each refuge sets its own rules.
The Caddo and LBJ National Grasslands are in North Texas. Rita Blanca (Panhandle) and Black Kettle (its Texas piece is at Lake Marvin near Canadian) are run from the Cibola office in New Mexico.
The Sam Houston, Davy Crockett, Angelina and Sabine National Forests are open to hunting. Some areas need an APH permit.
Many Corps lakes in Texas allow hunting on project lands. Some need a lake permit, so check with the lake office.
Colorado River Municipal Water District offers drawn hunts on its O.H. Ivie wildlife areas, and applications are usually taken in summer.
BLM land in Texas is limited and is managed by the BLM New Mexico State Office.