Well, it is actually made of leather on a wood frame. The wood frame provides the overall shape.
Mostly because leather is readily available wherever cattle are raised and horses are commonly use to work cattle.
However the internal frame of the saddle that provides its shape is wood and metals are used both to hold the saddle together and as decoration. In special parade saddles large amounts of silver (and sometimes some gold) almost completely cover the saddle.
It lasts a long time, is cool in the summer, warm in the winter, and gives the car some style.
The demand for saddles made from leather later declined with the advent of the industrial era
leather
Circle P saddles are made by Winntec and are made in Austraila. They are mostly synthetic as are the Winntec line and are lighter weight that regular all leather saddles.
Bicycle saddles were originally covered in leather because plastics had not yet been invented. Most modern saddles are, nowadays, made from composite (man-made) materials, either unpadded or padded with a gel for comfort. Traditionalistic cyclists' tend to still favour leather, using saddle-soap to keep the leather supple and waterproof.
Mostly leather from cattle, metal parts are usually steel.
cowboys and guachos
black leather
Saddles were made with wooden trees. Then, leather was use to make the seats, stirrups, and the girth. This is still the way many saddles today are made. They took a long time to make.
Oil is commonly used on leather saddles. The old is used to keep the leather from cracking and breaking. It also prevents the weathering of the saddle.
Saddles now a day are usually made out of leather. Ivory is illegal, what part would we even use it on? Usually all of the harder parts like the stirrups and the d rings are made of silver/iron/metal. Only very old ancient saddles would have ivory.
Blacksmiths set up shops to make and sell iron tools and saddles. The livery stable and the blacksmith were sometimes operated by the same person. The metal for the saddles was made by the blacksmith, and the leather was usually made by someone else.
The Brooks saddles are top-notch leather seats made for bicycles. The design of a Brooks saddle has leather stretched between metal known as "cantle plate".