I do two things.
First of all, Brooks makes a waterproof saddle cover, which I use cover my saddle. Since I have a leather saddle, I don't want it getting wet. The Brooks cover fits well, and stashes easily when I ride.
Second of all, I have a steel bike and prefer not to get it wetter than I have to. I use a tent footprint purchased during an REI garage sale. It was cheap because it fits a tent that they no longer carried. I use spring clothes pins to secure the footprint to the bike. I also carry parachute cored for a clothes line, so the clips do double duty. I could also probably rig a cooking vestibule if I needed to from the clothes line and clips. All multipurpose and all useful, and all easily stuffed in my panniers.