IMO, I always thought "Woody" was a troll or knome like work of art from a garage woodshop project that comes across as rather Fugly. But I could and others could classify myself as Fugly too.
Woody has gained ground in becoming a game day tradition, where the players rub it for good luck when they leave the bus. But as long as Woody does no harm then I say live and let rub (so go rub your woody everyone).