Apparently originally designed to hold automobile exhaust systems in their outstretched hands, many of these huge statues have been re-purposed to hold other items. Likewise, their clothing has been modified to fit their location.
The Full Throttle Saloon just east of Sturgis on Highway 34 utilizes a black shirted, cowboy hat-wearing muffler man holding a mug of beer and a cigar to welcome bikers to the Sturgis Motorcycle Rally. EDIT: The Full Throttle Saloon burned to the ground on September 8, 2015, but the muffler man survived. His and the saloon's future are uncertain.
More information about the muffler man phenomenon is available at RoadsideAmerica.com.