I have never noticed anything as far as my crossbow loosing accuracy, and such during cold weather, or even real hot weather.
I will say this though--lets say you had your crossbow, or weapon in the warm, and then out we go into really cold temps--I think that as materials cooling may be apt to issues until they equalize with the ambient outdoor temps--think about wooden gun stocks warping in extremes, or bow limbs de-laminating. Extremes in tamps. can do strange things to various materials.
I agree though with 1stlight--I sure react differently when temps go from 60 down to 10. My arthritis tells me that these low temps are not nice.--ha-ha
Thinking about it I think if you can slowly make the transition from hot to cold - say in the trunk of your car / bed of your truck while you drive to the stand and then the walk out rather than straight from the house and into the woods you may see less variation.