As stated above, you can carry a plastic grocery bag stuffed up under the seat between the leather and the rails to protect the bottom-side of the saddle in the rain - your tush will protect the top in the rain. When you get off the bike, if you're going to leave the bike parked outside in the rain, then drag the plastic bag out from under the seat and tie it over the top.

Actually, I find the seat bag that I carry my flat-fixing stuff in probably covers the bottom of the seat pretty well all by itself.

(Really, just don't worry. It's leather. It used to be a cow. Cows stand outside in the rain all the time.)