I routinely recommend icing necks and even heads. A response I get frequently is 'I've been doing heat.'

From my years of experience with joint injuries, I have always been told that icing is needed to reduce inflammation. Heat is used to increase blood flow for healing.

In many situations, healing can not even start until the inflammation is reduced to allow the strain on the joint to be resolved. If the ligaments are strained due to inflammation and the joint is not properly seated because it is locked up with spasm and inflammation, the only therapy for the short term is ice to reduce the inflammation.

A general rule of thumb has been ice for joints and heat for injured muscles.

At least this is what my PT and chiros have taught me.

Icing the upper neck can be very beneficial if those muscles are spasming. At the worst, the ice can reduce the pain of a head ache.

I have seen about 18 chiros, of which only 5 or 6 benefited me.
I have seen about the same number of PT's, of which only 5 or 6 benefited me.

Those that helped me also taught me how to help myself. Ice, the proper exercises, and behavior or posture modifications have all been repeated by the best professionals. The rest usually wanted me to leave all the decisions and therapy to them.

I've lived and learned.