Do a search for injector sticktion. Sounds like that is possibly your problem. Could be many other things as well, but as mark said the gp don't go out very often.
06 F-250 Lariat C.C too many mods to list
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Oil weight is important (15W40 could be too thick in winter if your injectors have a little stiction going on). Many recommend a 5W40 or 10W30 oil for winter. Don't go too long between oil changes. Flash updates to the processors help some w/ stiction and a product called Rev-X is said to be effective.
I have used amsoil, 5W30, since new w/bypass filter system, running three filters. I have also put a banks otto mind chip w/4" exhaust. The truck has 75,000 miles. No codes are found. It just starts rough until warm.
There is a small spool valve in the top of the injector that controls the flow of high oil pressure fed to the intensifier piston in the fuel injector. That spool valve only moves .017", back and forth, on and off every time the injector fires. Many factors play in to how well that valve works such as, oil temp, oil quality, normal wear, ambient temp, and many others. As this valve ages it polishes itself inside the bore of the spool valve and as the spool valve slams back and forth it can set up the condition like a suction cup, hanging the valve to one side or the other. This uncommanded uncontrollable condition is called stiction. Mostly its a rough run cold condition but in severe cases it can be a no start or pretty harsh misfire condition. Oil that stays inside the valve on a hot engine shutdown and is allowed to cool slowly in the injector can aggravate the condition on restart.
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