The Saddle Horn
The saddle horn is the most recognizable part of the western saddle. The horn is mounted on the saddle tree on the top of the fork and attached with screws and bolts. The horn consists of the cap (or head), the neck, and the points. (see diagram below)
The horn was originally added to the western saddle as a tool for roping cattle. When a rider ropes a steer, he can "snub" his end of the lariat around the horn to absorb the force generated when the steer hits the end of the rope.
Saddle horns come in many shapes and sizes depending on usage and preference. They are made of wood, steel, and brass and covered with rawhide. On roping and ranch saddles, you'll find an additional horn covering that protects the horn from the rigors of roping and provides a better grip for the rope. Horn wraps are made of a variety of materials including mulehide (a rough-out gray colored leather), rawhide or heavy latigo leather, and rubber - either black inner tube rubber or white Dura-Wrap rubber.
The horn is now a standard part of the western saddle, whether or not the saddle's used for roping. Over the years, a number of additional uses have been discovered for the saddle horn. It can be a handy hook to hang things on, a great spot to lean on when taking a rest, and, as so many have discovered, a security handle when the ride gets rough.
Horn diagram courtesy of Saddles by Russel H. Beatie