Looks like the real McCoy. Where is the rest of it?
Over the years I have owned several...down to just one now. It is a 1904 pattern with a centerfire rigging. Your saddle would have had the same quarter strap rigging.
The hole in the saddle was designed to keep pressure off the horse's spine and some say for cooling. This design allowed for the horse's loss of weight and conformation change that occured on extended campaigns.
I find the saddle comfortable to ride and the rigid deep seat helps keep you in the saddle. The only drawback is the rider is seated more vertically and just to the rear of the horses center of motion.
I only have one horse on the place that the saddle fits properly. Old Bullet.