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Blue smoke is generally cause by oil getting into the exhaust. The most common source on th 6.0 would be the turbo seals failing. It is possible to get blue smoke from injectors not firing properly, but this is usually accompanied by poor driveability and lose of power. Another source cold be a base engine concern, like piston rings or valve seals. You could have a crankcase pressure test done to determine the base engine condition.
You could have turbo seals leaking with no noticeable lose of power. It could be smoking more after sitting because the oil which is still in the turbo bearing housing when the truck is shut of slowly seaps past the seal and collects in the turbine side of the turbo. Although the other thing to note is if your getting the blue smoke on initial cold start then it may not be the turbo seals because the exhaust is not hot enough to burn the oil and create the blue smoke, this leads me to believe that the cause may be injector related.
Base engine concern should be consistent in smoke production, however if it something like a valve guide or seal (not common to the 6.0) it could be intermittent. How does this truck start, does it start rough or is it ice and smooth. If you try and drive down the road? When cold does it seem to lack power and blow more smoke?
OK there are a couple thing you will need to do. The first is to make sure the computer has the latest calibration from Ford programmed into it. The latest calibration has many improvements for cold start and driveability. After this is done if you still have the issue you will need to have a power balance test done on the truck on initial start to determine which injectors may not be functioning properly also should have a injector buzz test done this also test injector functionality. Next the FICM (fuel injection control module) will need to be monitored for proper voltage output to the injectors. I would highly recommend of reputable Ford dealer to perform these tests as they have the most experience with the 6.0.
Unfortunately there is no short answer for your concern as with the 6.0 diesel you need to cover all possibilities that can cause these concern. The 6.0 is a very finicky machine and 2003 was the first year for it and the most difficult to diag properly.