@LCDR what a great idea to store the blankets upright like a file! Genius long term storage idea.
During blanket season I store my blankets on a wall in my barn aisle. I have a series of large hooks set up high on the wall (as high as I can reach, basically). I put on/take off blankets over my horses heads so that I don’t have to undo the straps in the front and then I loop the front buckles over the hook on the wall and let the blankets hang from that. This way they dry and are out of the way.
I would never hang a blanket in the stall. One of my horses messes with everything he can get his teeth on.