Wrapping cling wrap, a piece of electrical tape over the muzzle, a muzzle mit, all help in keep moisture out of the barrel and compromising the charge. Also, keep the end of the muzzle down as much as possible.

If you walk in the rain with the rifle, at the end of they day, due to the conditions you were in, I would shoot it off. Then when you get home, take the barrel off, and clean the entire rifle. You will be nice and ready for the next day. And perhaps hope for better weather. Good luck to you.