I agree that it should not be normal, but my 2005 4.8is does the same.

If the temperature has been below 5 Deg Celsius overnight, on startup at idle it chugs like it wants to stall and shakes the whole car from side to side. Sometimes the Engine Management light comes on for a few seconds as well (flashes on and of for about 5sec then solid for about 10sec). If on startup I bring the revs up a bit to 2000RPM or so, for about 15-30 seconds it does not do this.

Had it to the dealer at least 3 times but they can't replicate it either, that said, they've never had it overnight and every time they looked at it almost right away so the engine would still have been warm. One of the times they said a misfire registered in the computer, but it was nothing to worry about. I am not convinced though.