Pat the prime rib roast dry with paper towels. Then place on a wire cooling rack set on top of a sheet tray. Generously season all sides of the roast with kosher salt. Refrigerate uncovered overnight to salt brine. See notes.
When ready to cook, heat grill or smoker to 180-200°F for smoking with your choice of wood or pellets. *If your grill has a super smoke mode, turn that on.
Make the horseradish garlic butter rub. Combine softened butter, horseradish, Worcestershire sauce, dijon mustard, mayo, garlic, and rosemary in a medium bowl. Mix together well and set aside.
Place the prime rib roast on the rotisserie rod. Slide the rotisserie rod through the center of the roast and press the forks into the meat (one fork on either end). Tighten the screws of the forks, or prepare the rotisserie according to manufacturer's instructions. Use butcher’s twine to tie the bones up against the rib roast if needed.
Spread on the horseradish rub. Next, slather on the horseradish rub, taking care to evenly cover all sides of the roast. If you're using a bone-in roast, then you can omit the rub on the bone side. Then season with freshly cracked black pepper. *The recipe for the horseradish garlic butter rub is just the right amount for a 6-7 pound, three bone roast. If your roast is larger than that, you may want to double the recipe.
Attach the rotisserie rod to the motor/attachment according to instructions. Start the rotation and close the grill lid. Smoke the rib roast at 180-200°F for the first hour.
After one hour, adjust the grill temperature to 325°F. Continue cooking on the rotisserie until the internal temperature hits about 118-120°F for medium rare, or a few degrees hotter for a higher doneness. *The internal temperature of the roast will continue to rise after you take it off the grill due to carryover cooking, so don’t bring the temp up too high on the grill or your finished roast will be overcooked.
Rest and slice to serve. After removing the rotisserie spit from the grill or smoker, let the roast rest for 20-30 minutes. Then use a large knife and cut the roast into individual steaks, about 1/2″ to 1″ thick depending on your preference. Serve with horseradish cream sauce, au jus, or your favorite prime rib accompaniments.