The question has a false premise for this animal
"Where do cockroaches go in winter" assumes there's somewhere for them to go — a hiding spot, a dormant state, a seasonal retreat. For the German cockroach, the species behind almost every home roach problem in New Hampshire, that premise doesn't apply. It doesn't go anywhere because it never left in the first place; it's an entirely indoor animal with no outdoor population and no seasonal cycle of any kind. The honest answer to the question, for this species, is that the question doesn't quite make sense.

