Pull the husks up to cover the ears of corn, and place the corn in a large bowl or pot. Cover the corn 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, melted butter, lime juice, milk, salt, and pepper, to taste 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, about 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 sour cream mixture. Divide the cheese evenly among the ears of corn, coating them on all sides. Serve immediately.