I had my 4.8is in the shop for the same issue last winter. They changed the levers, camshafts, eccentric shafts, plugs and some other stuff. Turned out to be a 6k € repair that DIDN'T fix the issue. Same rough start on cold mornings.

Then they exchanged some other part, which they didn't (want) to tell me, and the rough idle was almost gone. I think the changed or sealed the elbow of the air intake (edit: 10€ part??!).

So far this winter, I haven't had any (very) rough idle start, only sometimes a little rumble, when I put it in gear.

BTW, your FYI above is interesting! It could explain some of the engine behavior getting worse, when I put it in gear. Funny enough the engine doesn't recover, when I put it back to neutral??!

sharing on my cold start rough idling solution
 

Hi guys!
I posted this before on a different thread but would like to post it again here, I would like to share my experience on my previous rough idling problem during cold starts, now solved and hope that this could help someone with same case. My car is 2000 X5 4.4i E53 engine.

1) I cleaned the throttle using carb cleaner and tissue paper. I replaced the part #2 o-ring seen below
http://www.realoem.com/bmw/diagrams/u/u/301.png
2) I cleaned the MAP with carb cleaner spray.
(blow dried the MAP using hair dryer before placing back)

3) Replace item 11 (see below - as advised by my friend at BMW service center, this part usually causes major leak resulting to rough idling)
http://www.realoem.com/bmw/diagrams/j/f/79.png
4) Placed screw clamp on the small vacum hose attached at bottom side of part 12 above. (hose at end is already loose)

I might be just lucky, but the above solved my rough idling and till now i am having smooth run.

Do you think an Oil pan Heater pad would take care of the issue?

He's in Qatar, I don't think heat is an issue.

Diagrams no longer appear for this post. What parts are being referenced by point #3 ("replace item #11") and point #4 ("bottom side of part 12 above")?