If you're worried about the appearance of your clearly neglected saddle, buy some neat foot oil from your local saddlery (more £$%^&* horses), pour the contents of the can into a baking dish or a bowl large enough to take the saddle and soak first the top and then bottom in the neat foot oil, 10-20 minutes per side.
This could be useful some day. When you say top/bottom, does that mean you are first putting the whole top half of the saddle in oil and therefore also soaking the underside? After both sides are done, the entire saddle has been submerged in oil. After that, do you wipe off excess oil... and then let dry for a few days?
Thanks, Mike
edit, our saddles have always received TLC, just thought this soaking might be good to know about.