I often have a little purse/pocket-sized poncho in my suitcase that I can easily carry-about in case of showers. But the times I've forgotten or it rained more heavily, more often, I head over to the hardware store and pick up an inexpensive yellow rainslicker. I give it to a local before I leave. By the same token, one year while down at Christmas, a travel companion gave me a small collapsable umbrella as a gift. It came in quite handy that year. You can buy them pretty inexpenisvley at home and leave it behind when you leave too, if you are so inclined to do so. We've also found ourselves out walking about in a downpour, and all we did was laugh.
More importantly you'll want shoes that can withstand a little mud.