Basics I'd do are double layer of masking tape over the muzzle, keep the muzzle down lower than the lock, keep the lock up under the flap of the coat, etc.
IMO, the effects on deer from really severe weather changes are hard to predict...at least at your latitude, the rut should be over and that "behavior wild card" is pretty much out of the equation.
If it were me...(and I could actually get out from under the electric blanket and go out in that WX)...I'd look to get down in some low ground out of the wind and as close to a food source as possible.
If it meant sitting down overlooking a trail in a narrow ravine out of the wind, that's what I'd probably do...particularly if it led to a cutover cornfield or something that they might try to get to right at dark.
It's hard for me to compare mild climate North Carolina to what's going on right now in your part of the country...maybe folks from your locale can comment better...good luck.