A woody towel is the bar rag male bartenders tuck in the front of the britches supposedly for wiping off their hands. In reality it is to cover their "wood" as in "I would love to..." when face to face with a hottie or face to flesh with a pair of mounds more than a mouthful. It conveniently covers the bulge, re-adjustment, as well as subtle massage in an inconspicious manner under the guise of wiping one's hands.
With the nipples pressing to escape the fabric in front of the bartender's eyes, the bar rag in the back pocket was subtley switched to the front, thus becoming a woody towel.