Hunting in ND in Dec will not have any effect on your bow, your muscles however could be another story. When the shot presents itself after sitting still for a few hours in the cold your muscles tend to be quite stiff. When you can, draw your bow back and hold for a few counts, this will help keep the muscles warmed up and you can practice hitting full draw.
I am actually looking forward to the late hunt this year, with a large precentage of the corn still in the fields here in ND the rifle hunters are having a tough time finding deer. One more weekend of rifle season... then it's time to get back out there.
Your bow will be just fine.