Is it common? yeah kind of. Is it right? No. 90% of the time it's either weak batteries or a dying FICM. FICM test procedure is found at the top of the 6.0 page.
They do cut fueling etc when they're cold to save themselves.
Also, every diesel will run a little less than great when they're cold, since they need heat to burn the fuel efficiently. Also, especially on 6.0's and 7.3's because our injectors are fired off of the oil, as it heats up and thins out it moves much easier and allows the injectors to fire at the right times, and also you'll notice turbos are slower to spool with cold oil, as the oil thins up again, turbo can spool easier as the bearings aren't being dragged as much with cold oil.