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new expert. we need to make sure all the tires are within 1/4 inch out side circumference. I have seen these explorers have wind up issues when the tires get replaced and some are 1/4 inch or more different. These need all the tires replaced at the same time. Many people have TPMS (tire pressure monitor system) lights go on in the cold temps, this could be the tire issue we are having.
let me know what you find
one other thing to check. There is a bulletin(06-4-4) for the rear differential clutches. On turns it can cause the vehicle to a chatter, shudder or binding sensation. I had one give me a hard time a few years ago, felt it in the steering wheel. The vibration travels through the whole drive train , through the front suspension and can go to the driver at the steering wheel. These are know for bearing noises and these clutches in the rear differential. I would take a sample of the fluid. If not too bad you can try to change the fluid and add the friction modifier. These take 75-140 synthetic(23$ a quart) 3 quarts and 1 modifier. since the rear is independant suspension the differential has to come out for ths job.
I could see the 4x4 actuator cause this if it is weak and the fluid gets thick and it is in auto 4x4. You should try to leave it in 4x4 high when cold and see if it still makes the noise/binds.