Carpet works nicely, as does the spray on bed liner type product. Both of these come in many colors, and protect your paint job.
I'm having my Sundowner redone and the bed liner type is what I am having put in.
And the cork comes in rolls too, as many people will put it up in bedrooms for the kids to use as bulletin boards.
You can also sew something in denim to "button" over the bridle hook/rack and let hang down. Can add Velcro so that you could pull it up over the bridles so they wouldn't get dusty.
Horses make me a better person.