This means they have to be unbuckled and unthreaded to be removed from the saddle. This is called a stirrup suspension bar. The Patrol and Supreme have stirrup suspension bars. Saddle makers have been stuffing panels for centuries. Originally, doe hair was used but as that became difficult to obtain, hair from more commonly slaughtered animals grew popular.
Today stuffing materials include a range of acrylics.
There are pluses and minuses to using natural fibers versus man-made fibers. The plus side of natural hair is that it is cool on the horse's back. In the saddle, the hair acts much as it did when it was on the back of a living animal. Another plus to animal hair is that it conforms more quickly to the shape of the horse - the basic reason stuffing is used in the first place. Because once it does pack rock-hard, it must be replaced.