Have you checked the factory technical service bulletins for any information regarding this problem.
It sounds like your vehicle has been well maintained, and most of the obvious stuff has been checked.
Like battery connections, ground connections,fuses, previous repair to the system your having a problem with.ETC
If I had to repair your car, I would start by connecting a good
scanner with live data read out. set it to record mode recording each wheel speed sensor.
if nothing jumped out at me I would dive in to the numerous TSBs and see if anything was addressed for the AWD system, traction control or any other related system.
The cold weather your speaking of must be real cold weather not like what I experience in Florida, This may lead me to suspect a part with a printed circuit board that may have bad solder connections.
here is a link to what I am talking about if you have never played around with repairing printed circuit boards.
http://www.q45.org/timers.html
I have had much success in the past when my diagnostics led me to a expensive electronic item ECM BCM module relay etc where I had the choice to install a expensive part and hope that part fixes it.
Or take that item apart inspecting it closely with very large lighted magnifying glass. and checking it closely for cold solder joints ( AKA bad solder connections)
Typically these faulty connections will do like your experiencing, in warmer weather the solder is slightly larger making a better connection, in cold weather the solder will shrink some rearing its ugly head.
If you scroll down on the link I provided you will see some module this guy has taken apart I am not even sure what it is he is working on or how he repairs the bad connections. I provided this link because he took some good shots of the bad connections I am speaking of.
What your looking for on the back of the PCB (printed circuit board ) where the electronics, resistors capacitors etc penetrate the board when installed each connector is soldered using a solder bath technology and the excess leads are trimmed off, your are left with a mini hershy kiss shaped ball of solder surrounding the wire, poking through the board connecting the board to the part with this ball of solder.
After time of heating and cooling of the circuit adding vibrations to the mix, the less than desirable not hand soldered connection will fail.
leaving a fine hair line crack all the way around the ball of solder. easily seen in some of the pictures if you cannot easily find these pictures let me know and I will post just one picture with the bad connections.
normally if your lucky and catch it at the stage where the problem is intermittent you can re solder these bad connectors and not likely have the problem again and not spend more than a few bucks on the repair.
Most people will wait until the problem gets worse or become permanent, if this happens the bad connection with the added resistance to the circuit will heat up the board where the bad connections are resulting in burnt parts, sometimes a cheap resistor or capacitor that can be easily found and replaced. other times the parts are propitiatory and can only be purchased in bulk by a authorized service center or manufacturer.
The key here is, fix this problem before it becomes permanent and expensive.
The hard part is which part do you check for these bad connections?
This is where things have to remain simple and do not over complicate the problem or make new problems while diagnosing the problem.
Do not misread what I am saying I am not jumping to the conclusion that your problem is a bad solder connection but the symptoms make me think of the hundreds of parts I did repair both from the automotive field and electronic repair field.
If I haven't lost you by now and we are on the same page, great.
Some how some way we have to determine which tooth to pull.
So like I said earlier start with checking the computer with a good
scan tool for anything obvious, this will require more than just a code reader.
If this is not in your budget or technical abilities, it will be much harder for you but not impossible.
without the proper
scan tool, you have to research the TSBs that I mentioned earlier.
if you find anything close to the problem your experiencing this will give you an idea where to start looking.
If the TSBs have nothing even close to your reported problem, I would disconnect the battery remove each and every fuse from the fuse box one by one clean the bladed of the fuse and reinsert it. same thing with each and every relay. It doesn't matter if the fuse is labeled rear tail lights clean it anyways.
Next with the battery still disconnected check the switch if there is one to turn the AWD system off. cycle it a few times does it engage disengage properly? check all the wiring harness connectors that you can get to especially ones that have been removed or would have been removed during servicing or repairs that have been done.
you would be looking for connectors that have broken retaining clips at the connectors and are not plugged in properly.
Normally I would suggest a wiggle test to see if you can duplicate the problem by wiggling on wires and tapping on computers and modules etc.
Yet I am not sure how you would do this while driving.
Let me make myself perfectly clear before you attempt any of what I have said, I have never ever opened up a hood of your, year make model car that I can remember , at least for nothing more than basic service, because I stopped working on cars when your car was still fairly new and wouldn't have had these problems yet.
I will help more but I want you to read all of this, and if your willing to go further I will as well. Continued on second post this is too long for one post LOL