I carry a shower cap with me in my saddle bag. When I park my bike to go into work and it looks like rain, I always cover my leather saddle with the shower cap.
Then, when I come out of work and the world is wet from rain, I walk over to my bicycle and lift off the shower cap.
Everything in the world is wet except my leather saddle. It looks so dry and comfortable and warm.
The experience is like taking the lid off of a thermos of hot coffee when you are outside on a cold day and the warmth comes up to greet you.