Pour water, apple juice, cider vinegar, molasses, kosher salt, pickling spice, and black peppercorns in a saucepan; bring to a boil, stirring to dissolve salt and molasses. Simmer to blend flavors, about 5 minutes. Pour 2 cups ice into brine and stir to melt ice and cool brine.
Place pork loin into a large container and pack 2 more cups ice, or as needed, around the meat. Pour brine over ice and pork, cover, and refrigerate at least 4 hours to overnight.
Remove pork roast from brine and place into a slow cooker; pour 2 cups brine over the meat. Discard remaining brine. Spread sauerkraut, onion slices, brown sugar, fennel seeds, and coriander over pork roast. Set cooker on Low and cook for 3 hours. Add carrots to slow cooker and cook 1 more hour; add apples, cranberries, and walnuts and cook until an instant-read meat thermometer inserted into the thickest part of the roast reads 160 degrees F (70 degrees C), about 1 hour more.