Try not to worry about the cold, they're really much hardier than you think. Mine all ignore nest boxes too, and when we had snow back in march they were poking their heads out to try and reach as much as possible! They will lay whereever they happen to be when an egg comes (i've seen them walk along and an egg drop out without so much as a squat!). I have a few who will lay in the "bed" section of their hutches, and for those in:

this house I put down that pink tray of shavings (actually for a dust bath not a laying tray!), most lay in there but some in the upstairs box and some on the concrete.
Your housing looks perfect - quail are just a little dim
