Mix yogurt, fresh lime juice, chile powder, and coarse kosher salt in small bowl to blend. Can be made 6 hours ahead. Cover and chill.
Prepare barbecue (medium heat). Remove outer husks from corn, leaving inner pale green husks attached. Fold back inner husks; remove corn silk. Sprinkle corn with salt and pepper. Rewrap inner husks around corn. Grill corn until husks are charred and beginning to pull away and corn is tender, turning frequently, about 10 minutes. Grill lime quarters until lightly charred, about 5 minutes.
Pull husks away from corn to expose kernels. Place corn and lime on platter. Brush corn with crema-lime mixture. Sprinkle with cilantro.
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