Thanks William. I think I will wrap the box in a quilt, then cover with poly so the quilt doesn't become a sodden ice cube come spring (or even over winter where our temps seem to fluctuate a lot. They are on the north north east side of the house and the sun has already moved around to come up more southerly and less easterly but even then the sun is so weak and the temps so low (again in the 12F 11C) that it shouldn't pose a problem.
I don't have a compost pile. All garden detritus is ground up and put back on the beds for mulch to break down over winter. But you did remind me that I do have a mouse population that might view the box, even though filled with soil, a nice winter home with lots of vegies (lily bulbs) to feed on.