I have 2 coated wooden drying racks that I set up in a corner of our spare bedroom when needed. Once baby comes, this will not be a "spare" room anymore! I think then the racks will be in our bedroom, or in baby's room until/if he's over co-sleeping. In winter, things do dry pretty quickly due to the dry air in the house. (we keep our heat at around 64-65 when we're home, 60 at night) Maybe I'll be forced to put clothes away more often then, bc now, things stay on the rack until I wear the clothes, or I need to hang up more wet laundry!
I also hang things that go on hangers right away. they dry on the hanger, and then go right in the closet- these get perched on corners of the drying racks, or on door handles, closet doors, etc in the spare room, and in the basement if I'm desperate. (our basement always smells a bit damp...)
I think PPs have a good idea about drying overnight in a common space if possible.