Your horse saddle needs to have a dry solid space to be placed on while not in use. And while it may look nice hanging a saddle over a fence, it’s not very practical. You will need a saddle rack to get your saddle out of weather and dirt. This saddle rack is doubly interesting. It’s foldable and wall mounted and therefore very space saving.
I used to transport horses in trailers to different horse shows and competitions back in Switzerland. I had a folding saddle rack mounted on the door of the trailer. When out of use I just folded it flat down and it was out of the way.