Mike,
Living in Fairbanks, I encounter similar temperatures to where you are at.
Over the last 15 years, I have shot my Wes Wallace bows several times at -40C/F and as cold as -53F (-47C) last winter.
As previously mentioned, I tend to "warm-up" my bow by a couple half-draws, but I have never had an issue with any of my bows. Wes told me to avoid heat/cold/heat/cold. He said once it is cold soaked, keep it cold until finished.
I have literally shattered rubber blunts on more than one occasion, and have had numerous tips come off while stumpin' in these temperatures.
My biggest concern with hunting in these temps would be getting the animal field dressed. My plan is to build a fire (if able) as close to the downed animal as possible.
Good luck!
Jeff Cooper