We don't have anywhere NEAR as many blankets as you - only 5 - but we do the Ziplocks and stack them on a porch swing hanging in the barn :p good Burt cushions! In the winter we just don't put them in the bags. But we have 3 barn cats. No mice. ;)
I just posted this in responce to a question in the tack room thread but thought I would post this here since its applicable.
At my old barn they use these exact same racks and we just designated one stall as the "Blanket room" and these racks just lined the wall. Because we hung them up so high and the grain room was next door, we put the barn cats water and and bed under the hanging blanket, and we hever had problems with mice.
I love and swear by the Swinging Rug Rack from Dover. Because the racks are square and not simply long and skinny they help to keep the blankets shape, and they make it SOO much easier to flip through your hanging blankets. The square rack keeps the whithers and back part straight so it doesn't get all crumpled http://www.doversaddlery.com/swinging-rug-rack-3-arms/p/X1-27065/
I hung a chicken lamp above them and am using a bathroom heat bulb to help dry them faster in the spring and fall rainy seasons, or I turn them inside out to warm the blankets up in the winter. (Don't use the infrared bulbs for chicks; infrared doesn't heat up fabric or evaporate the water as fast.)
All of these blankets are 84" which is why they're hung so high: