My view is, +1 on Randy's black bag approach to re-oiling the saddle - Use of Proofide rather than all of the other stuff that's out there, and +1 on gently warming the saddle. However here southern Michigan November has brought us almost freezing temperatures, though we have some sun, y'all!
But before that, I also agree with cleaning. First saddle soap with warmish water and a soft sponge to get off the loose stuff. If at that point you can see mildew, try repeating with a dilute bleach solution to kill the fungus. There are Internet articles about mildew treatment of leather - it can grow back.
Look for cracks, crazing, pulling at the rivets, and rust on the steel frame underneath. You could ust replace teh leather. List member rmayr is an expert at doing that.
The saddle looks like it might be an early Team Professional, due to the big rivets. I remember seeing those Turin bikes in the store but with cheaper parts, at least the ones that were plain steel tubing. Based on the parts and non-Reynolds frames, I equated them with Peugeot UO-8s, which only would come with Brooks Pro for a store upgrade. If you restore it to pretty good condition, it would be a very worthwhile saddle for any level of bike. If it is a Professional, it would say "professional" on teh side skirts.