The certificated private pilot was landing a tundra tire equipped Piper PA-18 airplane on a dry, paved runway, which required a correction for a left crosswind. After touchdown, during the landing roll, the airplane veered to the left. The pilot applied right rudder and right brake to correct the veer. The airplane pivoted 180 degrees to the right, and the right wing struck the runway. The airplane sustained substantial damage to the right wing leading edge, and right wing main spar.