QDII has limited slip differentials, the axle fluid has friction modifier added to it to preven the clutches in the differential from making noise and engaging too harshly.
I've seen more than one folk with QDII post about this problem, then reported fresh axle fluid with the proper friction modifier added to it solved the problem. The cold is likely making the problem worse till the fluid warms up.
Check what you're Owner Manual says, I "think" it says for the severe duty schedule to change the axle fluid every 15k miles, for normal service I "think" it says you don't have to change the axle fluid. If you drive like a little old lady, only sunny spring days, you can use the normal service schedule. You off road, drive in snow, drive more than once or twice in severe cold, drive short distances everyday, etc, you should use the severe duty schedule.
Personally for myself I use the severe duty schedule, BUT, my driving and conditions fall just short of that, so I'm modify it a bit with the axle fluid change, I'd go broke changing axle fluid that often. I use AMSOIL axle fluid and change it every 60k miles.
Remember use what the OM says, I "think" its Synthetic 75W-140 Gear Oil and Mopar Friction Modifier of a certain amount.