Trim pork roast. Rinse and pat dry. Sprinkle with Smoky-Sweet BBQ Rub; let stand at room temperature 30 minutes.
Bring internal temperature of smoker to 225° to 250° according to manufacturer's directions, and maintain temperature 15 to 20 minutes.
Place pork, fattier side up, on cooking grate directly over coals in center of smoker. Cover with lid, and adjust ventilation to maintain temperature between 225° and 250°. Smoke, covered with lid and maintaining temperature, 5 hours; turn pork, fattier side down, and smoke 2 to 3 more hours or until a meat thermometer inserted into thickest portion registers 195°.
Transfer to a cutting board; cool 15 minutes. Shred pork.