I would say that at 40 below zero your rifle has as much chance of freezing and failing as your bow does. I would be concerned about the arrows though. I would guess they would perform much differently at 40 below zero than they would at normal temperatures. I would be afraid they'd fly different and also maybe not penetrate as well. Another factor to consider is if you are wearing enough clothes to stay warm at that temp, can you pull back your bow?????