I don't think there is ever a time where icing can cause a problem unless hypothermia is a risk.

So, when in doubt, ice.

And, remember that icing is not a quick fix. It is part of a bigger picture of treatment. If it helps/feels good to ice a place on your head, then do it.

The icing of your neck is to reduce the inflammation at the sight of the adjustment. Once the area becomes inflamed, it takes more repetitions of icing to reduce it. If done right away after the adjustment, the inflammation can be prevented or at least limited. You should still ice periodically after the adjustment.