An alternate explanation as to the cause of brain freeze is that the cold that passes thru the throat causes the arteries to contract, diminishing the blood flow to the brain.
This is a plausible explanation to the layman (me) and I can't quite affirm that it is true. I have to bow to Starke's explanation, however, since my source is a non scientific publication: Stuff Magazine. I apologize for not being able to properly cite this, since I don't have that issue with me.