This subject is sorta “close to home”, given the very-winter weather we have been . . . enjoying . . . the last month or so. So I’ll toss in my comments just FWIW:
During the off season, winter turnouts are stored on a wall-mounted blanket rack mounted in a relatively low traffic corner of the barn. They share the space with the fly-sheets, some large boards and pieces of plywood, and a couple of automotive drive shafts hangin’ on nails.
When we are doing the “Blankies on, blankies off” routine, I just toss the garments over a convenient stall panel, in the sun if available, inside-out so they can dry off and air out a bit. I also fasten a couple of their straps around a rail at the bottom to prevent the wind, or the Equines from tossin’ them into the snow/mud/poop.
I only stock heavyweight blankets; my crew are furry enough (and they have access to stalls in the barn) that “normal” winter weather (~20°F low, 40°F high) doesn’t require blanketing for them to be comfortable. Honestly, tho, they all like their turnouts, and would, I’m sure, happily wear them 24/7 all winter long if that was in the game plan :-D.