There are small black rubber muzzle-covering "balloons" (sorta) that fit over your muzzle to keep water out but pose no risk of a bulged barrel supposedly. Never used them, but they would be fine for rifles. Now, shotguns might be another matter, don't know. A shotgun barrel is much more prone to bulging/bursting than a rifle. Again, I don't know.
Given enough water standing in a barrel upright, eventually enough moisture might cause problems. Certainly loading a charge in a wet barrel will contaminate your powder. Best keep the muzzle pointed down in a rain. Covers for hammer/frizzen/drum/etc. are available or easily made. Water's not a friend of black powder (except when cleaning).
