Well, a headache is when blood collects in your head I believe. Theoretically, anything that increases blood flow should help to get the excess blood out of your head. I would that that heat would work better than cold (unless there is some swelling or something... I dunno).

I don't, however, have any idea what causes a brain freeze, so... I don't know how that helps; if it works, though, spread the word.

What is it they say about silence being golden?