Google Horse rug storage bags and several companies should come up on the search, like Shires etc. There's even one company that personalises them. It's a pricey option though, a storage bag from Ikea or Dunelm would probably be cheaper.
Mine did too. I use "Dimpa" bags from Ikea. Â£2.99 each. Large enough for 2 heavy weight turnouts or 6 odd fleeces. (and pretty much everything in between...) Had the oldest of them about 3 years I think - still going strong.