The leather of the last snaffle bridle I bought was very tough. I applied some oil and let it "dry" for about 5 hours and it was much better after but I guess the leather quality is not really nice. The leather has to be quite supple, it is a sign of quality!
You can use oil! It can be vegetable oil, neat's foot oil and let the leather become soaked for some hours. Then remove the excess of oil with a dry rag. But don't forget to clean and grease your snaffle bridle every week or every two week to keep it supple :)