According to the pilot, during the landing roll, he noticed three deer enter the runway from his left. One of the deer stopped on runway centerline and the pilot stated that he steered the airplane to the right, missed the deer, lost control of the airplane, and departed the right side of the runway. The airplane collided with a runway marker sign. Post-accident examination of the airplane revealed substantial damage to the fuselage and left wing. The pilot reported no mechanical malfunctions or failures with the airplane that would have precluded normal operation.