Copied and pasted from TPWD website:
Exceptions: a hunting license is not required to hunt the following:
Coyotes, if the coyotes are attacking, about to attack, or have recently attacked livestock, domestic animals, or fowl.
Depredating feral hogs, if a landowner (resident or non-resident) or landowner's agent or lessee is taking feral hogs causing depredation on the landowner's land.
Fur-bearing animals, if the hunter possesses a trapper's license or if the fur-bearing animals are causing depredation.
Waylon, do as you like, but be prepared to articulate in a court of law, that the hogs were causing depredation.
Personally, I'll spend the money yearly on a liscense ($65 combo), as it helps our great state's hunting and fishing industry, and helps avoid any trouble.
Being the higest paying hunting contest in the State of Texas is what makes this contest so desireable.