Pull the husks up to cover the ears of corn, and place the corn in a large bowl or pot. Cover with cold water, and place a large plate or other weight on top of the corn so that it remains submerged. Allow the corn to soak for at least 1 hour or as long as 4 hours.
Meanwhile, combine the sour cream and milk in a small bowl, and set it aside.
Preheat a grill to medium-high. Adjust the grilling rack so that it sits about 4 inches away from the fire.
Drain the corn but do not remove the husks. Lay the corn on the grill and cook, turning it frequently, until it is crisp-tender, 15 to 20 minutes. Remove the corn from the grill and allow it to cool slightly. Then pull the husks back to form a handle, and brush the ears evenly with the melted butter. Squeeze the lime halves evenly over the ears of corn. Return the corn to the grill and cook, turning it occasionally, for 5 to 10 minutes, or until the corn is slightly browned in places. Remove the corn from the heat and brush the ears with some of the sour cream mixture. Divide the cheese evenly among the ears of corn, coating them on all sides. Sprinkle with the chili powder and kosher salt, and serve immediately.