It needs to warm up for a couple of minutes. I know that is not what you want to hear. but try that first. It is cheap. Maybe the EGR . Scan it for codes.
This is normal operation, the Exhaust Back Pressure Valve closes when the truck is started in cold weather. Once it warms up the EBPV opens and allows normal operation.
Oops. I don't know if the 6.0 is this way. The info I just posted relates to a 7.3.
my 05 wasnt that bad but the thing that helped the most for me was cleaning the egr and draining the water valve thing on your fuel filter on the frame rail sorry ive been out of touch for a while and not brushed up on my terminology yet. they also reflashed it at the dealership as a recall i also have beeen running a power adder since like 8k and i think thats helped me a l ot by keeping things cleaned up