Weather in December can be unpredictable. I have read about rides from Dallas to Austin but not sure about Fort Worth as a starting point. Last Friday a group of veterans finished a bike ride from Wichita Falls to Corpus Christi which might have went on a route you could take. I did not search for their route nor have I seen a website with the route. There several bike clubs along the route: Fort Worth Bicycling Association, Waco Bicycling Club and several in Austin that might have route information. Also crazyguyonabike.com: Bicycle Touring: A place for bicycle tourists and their journals probably has a journal of somebody that did a ride. A couple of months ago a biker rode from the Oklahoma state line to the Rio Grande Valley but I don't remember his route specifics but it was west of Fort Worth.