Stir cool water, salt, and sugar together in a large, clean stockpot until salt and sugar are completely dissolved. Submerge turkey in brine; cover and refrigerate for 8 to 14 hours.
Remove turkey from brine; rinse inside and out under cool running water for several minutes to remove all traces of salt. Pat dry with paper towels. Discard brine.
Preheat the oven to 450 degrees F (230 degrees C). Place turkey on a rack in a roasting pan.
Mix softened butter and pepper together in a small bowl; rub mixture under turkey skin. Brush melted butter onto turkey skin and pour wine into the pan.
Roast in the preheated oven for 25 minutes. Baste turkey and rotate the pan. Continue roasting until skin turns golden brown, about 25 minutes; baste again and rotate the pan.
Reduce the oven temperature to 325 degrees F (165 degrees C) and continue roasting, basting, and rotating the pan once more about halfway through the cooking time, until no longer pink at the bone and the juices run clear, 1 hour 45 minutes to 2 hours 15 minutes. An instant-read thermometer inserted into the thickest part of the thigh, near the bone, should read at least 165 degrees F (74 degrees C).
Remove from the oven and let stand for 20 minutes before carving.