Woodson is a town in Throckmorton County, Texas. United States. As of 2020, the population was 219. The area was initially settled in 1875 by J.O. Wood and Henry McClintick. Wood's son, O.J. Wood, played a leading role in the shaping of the community and its economics. Woodson was originally called Jom, when it was established around a cotton gi…Woodson is a town in Throckmorton County, Texas. United States. As of 2020, the population was 219. The area was initially settled in 1875 by J.O. Wood and Henry McClintick. Wood's son, O.J. Wood, played a leading role in the shaping of the community and its economics. Woodson was originally called Jom, when it was established around a cotton gin built so that the ranchers could get cottonseed to feed to cattle. After Jom was established, O.J. Wood deeded lots measuring 100 by 190 ft to anyone who would build a residence there, free of charge. This caused businesses to start popping up, as a post office and Wood and Sons grocery were established.