Wear a hat with a bill long enough to keep the water off of your shooting glasses. If it is a warm day, they will probably mist up real quick anyway.
Don't shoot Federal Papers, especially reloads, as some may swell and separate upon firing. If you absolutely have to shoot paper shells, keep them dry under a rain jacket until you load them into the action.
I was shooting Federal paper reloads once when it started to rain and when the shell fired, the front section of the hull separated from the base. I was able to pull a few separated hulls out of the chamber but, after a while, one separated hull went forward about 18" and became lodged in the barrel. I had to finish the round with a backup gun and plastic shells.
One thing about shooting in the rain, you can often see where your shot string goes.