I put my wine cap box in the unheated garage all winter in a bed of coffee grounds for inoculation, and it got down to about -20F (MN USA), so I'm wondering how much I hurt my fungi.
The container was in a plastic box with open air on top (carpenter shavings), and growth medium was kept moist. One of my friends from the local mycological society said that he was able to see some mycelium in the growth medium this fall.