It's not the cold that will break a bow. It's the drying out of the wood from repeated exposure to the cold, which tends to dry out wood by itself, then bringing the bow back in to the warm dry air of the house.
I was Deer hunting with an Elm recurve many years ago and it was a particularly cold Fall. After a week of this cold/warm cycle the back of the bow failed in tension as I was exercising it on my stand.