There are several designated off-reading areas in the state of Texas, including state forest lands, state parks, recreation areas, and the 85-mile-long Sam Houston Multiple-Use Trail. On public lands, for the most part, you can't ride your ATV off of designated trails or recreation areas, including road ways. Federal grasslands ban all cross-country (off-trail) use of ATVs for any reason, including game retrieval. So, if you're planning to use your ATV while hunting, plan accordingly.
Check out these Fredericksburg, TX ATV/OHV resources: