I don't believe "cold", by itself, will keep deer from moving. Look at it this way, the colder it gets, the more energy deer use just trying to maintain their body temperature. This means they need MORE food to keep them going. They've got to eat! Deer are less inclined to move during a storm or in very windy conditions.
Also, what we consider "cold" and what game animals consider "cold" might be two entirely different things. I've seen deer and elk doing their normal thing in temperatures way below zero. And elk, for example, aren't even comfortable until the temps get down to freezing. I had two hunter friends get frostbite, here in Montana, this year while hunting elk. One of them killed a 6x6 bull, and got frostbite while he was gutting it out. The other one wasn't so lucky! I watched football that day.