Actually, a good quality leather has to be quite supple. If it's too tough, don't buy this article. Tough leather can injure your horse when you ride.
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!
I also know Effax, it's nice. Oil is also effective but it takes more time. But don't use paraffin oil, it can damage the leather as it is a petro- chemical derivative and it it clogs the pores.
Alicia is right. Let the snaffle bridle in oil some hours if the leather is really stiff. It works with every type of oil: vegetable, animal, cooking oil... I like and use Effax's products.
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 :)