Naturally, the entire rifle must be clean, not just the breech plug. I have a very detailed post with cleaning instructions you can refer to: 13 Steps To Properly Clean Your Modern Muzzleloader.
Now while hunting in the rain, and I’ve hunted in some real down pours, I make efforts to keep the receiver under my rain gear. Beyond that I really haven’t found reason to do anything more. Course, after hunting in a real heavy rain all day, I choose not to tempt fate and will reload my rifle with a fresh load that night. But if it wasn’t pouring and I was sensible with my rifle, I leave the load in the barrel. (Maybe you’ve seen my extreme demonstration of a wet rifle in a pool in my CVA Accura video?)