Trim fat on pork shoulder roast to about 1/8 inch thick.
Sprinkle pork evenly with Barbecue Rub; rub thoroughly into meat. Wrap pork tightly with plastic wrap, and chill 8 hours.
Discard plastic wrap. Let pork stand at room temperature 1 hour.
Soak hickory chunks in water 1 hour.
Prepare smoker according to manufacturer's instructions, bringing internal temperature to 225° to 250°; maintain temperature for 15 to 20 minutes.
Drain wood chunks, and place on coals. Place pork on lower cooking grate, fat side up.
Spritz pork with apple juice each time charcoal or wood chunks are added to the smoker.
Smoke pork roast, maintaining the temperature inside smoker between 225° and 250°, for 6 hours or until a meat thermometer inserted horizontally into thickest portion of pork registers 170°. Remove pork from smoker, and place on a sheet of heavy-duty aluminum foil; spritz with apple juice. Wrap tightly, and return to smoker, and smoke 2 hours or until thermometer inserted horizontally into the thickest portion of pork registers 190°. Remove pork from smoker, and let stand 15 minutes. Remove bone, and chop pork.