Preheat the smoker to 250 degrees F.
Score the meat by using a sharp knife to cut diagonally on the fat.
Season the meat liberally with the garlic salt and the pepper, then let sit, about 15 minutes.
In a small mixing bowl, add the apple cider vinegar and the apple cider and whisk together, then transfer to a spray bottle.
Place the prepared pork on the grill of the smoker with the fat side up. Close the lid and cook, untouched, for 2 hours.
Spray the meat with the apple cider mixture every 30 minutes for the next 4 hours.
When the temperature of the meat reaches 165 degrees F, about 6 hours, transfer the meat from the smoker and wrap in tin foil with the fat side up.
Return to the smoker and cook until the internal temperature reaches 205 degrees F, at least another 3 hours.
Transfer the wrapped meat to a cooler, or a cooled oven, to rest, about 1 hour.
Transfer from the cooler and unwrap and remove the bone, then shred the pork with a pair forks.
Mix any remaining apple cider mixture from the spray bottle with the pulled pork and add the barbeque sauce.
Serve.