As far as I've seen when they say "chains required" it doesn't matter what you're driving, 4x4 or not...

I figure that if it comes down to it I can always tuck in behind a big rig and I should be alright. I'm going to have my wife's Cobalt on a trailer behind me also...

 

I am out chasing elk around the high country this time of year and most of the mountain double tracks have one to two feet of snow on them. When the 4X4 no longer makes it the chains do. I would recommend two sets of heavy duty V-Bar chains designed to take the torque of the Powerstroke. Here's a picture: V BAR TRUCK CHAINS They typically run around $120-$140/set and are stocked at most auto parts stores (at least here in the mountains). I have found that you should ALWAYS chain up all 4 tires or you will have issues keeping the truck on track. Chaining only the back gives poor steering, breaking and a lot of bounce/chatter with a light rear end. Chaining only the front allows the rear end to pass the front on steep downhills and provides poor breaking. The front clearance to the bumper is minimal for good heavy duty chains. The solution is to cut the bottom inside of the bumper off at a 45* angle and remove any obstruction to the chain as the tire turns. I know guys who have not done this and their front bumper now sits at a 45* angle down on the back side!

My daughter and I plowed up to 12,500' last weekend - with the chains it is almost like a snow cat. I keep a winch on the truck just for backup. No one is going to come rescue you and get your car out of the high country this time of year - you are on your own. It is snowing right now - I wish my daughter would wake up so we can get back out chasing the elk. We have our eyes on an Albino and two Calico elk in the herd we have been staking for the last two weeks. Probably be throwing the chains on again today...

 

I've got plenty of bumper clearance with my 3" body lift. We'll be staying on the major highways the whole way there.

 

With a 3" lift you will have no problem. Major highways - even passes in the mountains - 4X4 w/o chains is acceptable when chain law is in effect. If it gets worse than that they will just close the passes until it is cleared. If you want chains for backup anyway - get good heavy duty ones rated for the torque of the diesel. I have never in my lifetime of living high up in the mountains needed chains on a major "paved" road. Only time I ever use chains is on the unmaintained/unplowed back roads/forest service roads or off road.