When it is raining or snowing, and in the winter in general around here, I just put a plastic grocery bag over my saddle, and switch to wet-lube for my chain. Road dirt sticks to wet-lube more, but it does not wash off in bad weather, and you have to check your chain more often in wet weather anyway (1-2 times per week for me). I also put a dab of lithium or other heavy grease where my brake and shifting cables come into contact with the cable housings and stuff. Gotta keep those things rust-free.
That is about it. I don't have any serious issues with my tape staying wet, or anything. You only have to worry about the exposed steel parts, and most parts on yours an my bikes are aluminum or plastic. No big deal.