Kevin,
Have you contacted the Arkansas Grand Lodge directly to see if Colonel W.H. Martin was a member of the Masonic Lodge in Arkansas? To be guessing I would try membership rolls in Western Star Lodge #2. as for background information, General Patrick Cleburne was a very active Mason before the war. the book "Biographical Sketches of General Pat Cleburne and General TC Hindman" by Charles Edward Nash MD. explains alot about the work of Masonry in Arkansas at the time. Dr. Nash was a friend and business partner of Cleburne. Another masonic civil war legend that might give you background/insight was the death of General Lewis Armistead at Gettysburg.