In a small bowl, mix mild paprika, light brown sugar, hot paprika, celery salt, garlic salt, dry mustard, ground black pepper, onion powder, and salt. Rub spice mixture into the roast on all sides. Wrap in plastic wrap, and refrigerate 8 hours, or overnight.
Prepare a grill for indirect heat.
Sprinkle a handful of soaked wood over coals, or place in the smoker box of a gas grill. Place pork butt roast on the grate over a drip pan. Cover grill, and cook pork until pork is tender and shreds easily, about 6 hours. Check hourly, adding fresh coals and hickory chips as necessary to maintain heat and smoke.
Remove pork from heat and place on a cutting board. Allow the meat to cool approximately 15 minutes, then shred into bite-sized pieces using two forks. This requires patience.
In a medium bowl, whisk together cider vinegar, water, ketchup, brown sugar, salt, red pepper flakes, black pepper, and white pepper. Continue whisking until brown sugar and salt have dissolved. Place shredded pork and vinegar sauce in a large roasting pan, and stir to coat pork. Serve immediately, or cover and keep warm on the grill for up to one hour until serving.