Have you tried that fabric freshener stuff that's out there called Fabreze? I know there are a few variations of it, supposedly for various purposes. I have used this "Fabreze Extra Strength"......"for carpets, fabric and air" for a few things and I've been surprised at how well it worked.
Here is a pretty good recipe for a deodorizer, however, Iwould try the Fabreze first to see if that does the trick. In either case, look at the last paragraph, below and follow that as far as application method and procedure:
Homemade Deodorizer Recipe
1/2 cup household hydrogen peroxide
1 level Tablespoon baking soda
2 Tablespoons white household vinegar.
1/2 cup water.
Put this in a spray bottle
Mist the Fabreze or the homemade recipe all over the saddle, being sure to get up under the skirts and into the nooks and crannies. Put the saddle outside to dry in the sun. After it's dry, flip it over and let it stay outside in the sun for several hours. If the saddle has a sheepskin lining underneath, especially let it stay in the sun several hours and reapply the soulution after a couple hours, massaging it well into the sheepskin wool. In this case, it's not just the deodorizer that is working, but also being out in the sunlight, which is a natural odor killer.