I don't know of any contests in Texas. There are however two or three in Lousiana (Winnfield is the biggest one, there's a couple smalller ones, but I can't remember the names of the towns), two or three in Arkansas (Fordyce, Taylor, and Sheridan), two or three in Alabama (Jackson is the only one that stands out to me).
I hope that helps. Do a google on North American Lumberjack Guide. i"m certain there's a listing of the contests on that website.
All the best,
jamie