I have an storage area in our (heated) garage, right next to the furnace, which has a closet bar in it. I hang dry our clothes (on hangers) in there year-round. Even when it's -40, the heat from the furnace keeps it warm enough to dry. Any overflow gets hung up on the shower curtain rod, again on hangers. It works really, really well. I can even take a couple of pants hangers (with the clips) and hang dry our sheets that way.
But we also live in a very dry area so I'm not sure if this would work as well in, say, the Pacific Northwest. :)