I have a 04 6.0 and when I first start it up it idles great but when I start driving it at around 50 mph it has a really bad studder. I step on the accelerator a little and then it stops then when it comes to a stop it like its misfiring only does it when it's cold once it warms up it's fine.

 

Sounds like sticky injectors to me.

I would start by having your batteries load tested. Both of them. If one is bad, replace both.

Next, test your FICM. You can find the test procedure at the top of the 6.0 page in the "sticky" section.

Then if it's still doing it and FICM/batteries are good. Try adding some Rev-x. Should clear that right up.