Prepare the corn for grilling by gently pulling back the husks and removing the silk (do not remove the husks). Place the corn in a shallow dish and cover with water; soak for 30 minutes.
Heat your grill to medium and arrange the corn on the grates in a single layer. Cover and grill for 20 minutes, turning every 5 minutes. Transfer to a plate and let cool slightly; remove and discard the husks.
If desired, remove the husks and return the corn to the grill for 5-7 minutes or until lightly charred.
While the corn is cooking, mix together the goat cheese, milk, and lime juice until it has a consistency resembling yogurt. Season with salt.
Spread each piece of corn evenly with about 1 tablespoon of the goat cheese spread. Sprinkle with smoked paprika, chipotle chili powder, and chopped cilantro (if desired.) Serve with lime wedges.