Working with one ear of corn at a time, peel back the husks to expose the kernels, leaving husks attached at the base; remove the silk threads and tie husks together with kitchen twine around base of cob to form a handle. Repeat with remaining ears. Transfer corn to a large bowl or pot of water and let soak for 30 minutes. Build a medium-hot fire in a charcoal grill or heat a gas grill over medium-high heat. Transfer corn to grill; cook, turning occasionally, until charred and cooked through, about 20 minutes. Remove corn from grill and brush with mayonnaise. Place cheese on a plate and roll each ear of corn in cheese to coat. Sprinkle corn evenly with some of the cilantro, chile powder, and salt and pepper, pressing the corn so that seasonings and cheese will adhere to the mayonnaise. Serve with lime wedges.