Your bow will shoot a little different at 40 below. We have practiced out in that temperature, and I have gone hunting in temperatures colder than that. Heck, we are at 60 below chills right now!
The rubber on the bow will harden, so a couple things will be affected there. If he is shooting with harmonic dampners (not sure on the Z-Max) they will harden up and become nearly useless. He might want to try shooting without them. Also, if he is using a quiver with rubber on it, he will have a very hard time extracting the arrow from the quiver. I could barely get mine off last month when I was trying to get a shot on a fox after a hour long stalk on the little bugger.
He will want to practice in the clothes that he is going to be wearing, and it would probably be best to shoot a few arrows after the bow has time to acclimate to the weather. At 40 below that should only take a couple of minutes, but he should try and practice in as real life conditions as he will have when he gets on a bou.
I've never done rifles at those temps, so I couldn't give my 2 cents on that.
It doesn't take long to die in those temps, and skin can freeze in a minute, literally, so he should take everything as serious as possible.
ArcticBowMan's Hunting Photo's