Place corn back in their husks in a large pot of water and soak for 2 hours. Soak wood chips in another container of water for about 30 minutes.
Preheat a smoker to 250 degrees F (120 degrees C). Place corn, unstacked, onto wire racks. Place the racks into the smoker. Add wood chips according to manufacturer's directions. Smoke until corn reaches your desired level of tenderness, 60 to 75 minutes.
Combine butter, cilantro, lime juice, lime zest, and paprika in a small bowl. Peel back the husks and brush corn with the butter mixture. Season with salt and pepper.
