My wife had a clothing piece that was hard saddle type leather that she dyed a deep red. She used a dye that specifically called out that it was for leather. I can't remember the name, but the packaging looks like it hasn't changed since 1952. Some Google searches may find something.
First, she dyed the leather. Then, she used a clear polish which helped smooth out the slightly inconsistent results of the dye, making it very nice looking. The piece was very thick stiff leather, so I don't see why it wouldn't work for a saddle.
EDIT: My wife found it for me. It's called Angelus. Buy the reducer, the finish, and some daubers. She bought them from Dharma Trading Co., and the whole thing came to about $7. It was very cheap, and worked well.