Winnebago Won't Start in Morning & Damp Outside

You are getting some condensate (moisture) in the electrical system somewhere. Start by unplugging any connections to the distributer, applying dielectric grease to the connections and plugging them back in. If there are connections to the spark control, do the same there. Also, it could be a failing coil, or a bad secondary wire (high voltage, spark plug wire). It starts later because the moisture dries out, and allows the correct path for electrical continuity.