So-called secret societies are often far from it; the Freemasons have websites and lodges are easily found. If you are looking for sinister machinations you're better off looking at Fortune 500 companies (or Enron -- those people could conspire!)
The history of these groups springs from filling a very public need: as a benefit of membership, the Masons and the lesser-known Oddfellows in the past have provided health and social services. In Houston, the long-gone Masonic Cemetery (established by Holland Lodge #1) was the final resting spot for many notable Texans, including Anson Jones (last president of the Republic of Texas and both a Masonic and Oddfellow Grand Master.)
The publicly inaccessible archives of the Ancient Free & Accepted Masons Holland Lodge #1, 4911 Montrose Ave., are filled with portraits of Masonic Texans, all of whom participated in the formation of Texas. Sam Houston (president of the Republic of Texas, founding member of Holland Lodge), M. B. Lamar (president of the Republic of Texas, member of Harmony Lodge No. 6, Galveston), Stephen F. Austin, James Bowie (hero of the Alamo), William B. Travis, James W. Fannin, Jr. (member of Holland Lodge), and David "Davey" Crockett (hero of the Alamo). The lodge access is members-only, so it is up to the Oddfellows to be the secret society with an open door policy, at least in the basement.
In the bottom floor of Oddfellows Lodge #225 is the David G. Burnet Museum of Texas History, dedicated to "showcasing the role of Odd Fellowship in the founding of the state of Texas." Seeing that Burnet's life (1788-1870) coincided with Texas' formation and struggle for independence, the museum would be poised to be a fountain of information about this man and his instrumental role in Texas history.
That is, if it was ever open.
While the museum is talked about and pictured on the lodge's website, the doors are always closed. Through the windows, the exhibit can be seen laid out, awaiting visitors. The Heights Lodge looks to eventually open the museum up, but illness has slowed its progress.
Until the Oddfellows' doors are finally open, the Handbook of Texas Online and Wikipedia entries on David G. Burnett will have to tide the curious over. Lastly, for those with a fear of secret societies, be happy that their past conspiring succeeded, for the Texas you know and love wouldn't exist without them.