Is there such a thing as brain freeze?

While window-shopping, Wyng walked next to me and held my hand.

Wyng: Mommy, do you know that there is no such thing as a brain freeze?

Mom : Yeah, the brain doesn't freeze. (Mom has to say this as it is a fact, isn't it?)

Wyng: It's just the blood vessels at the roof of the mouth that expand and when blood rush in the blood vessels, we feel like a pain. Our brain does not have any pain sensors. So there is no brain freeze.

Mom's mind is thinking,"Really?". Thanks to all the science documentary programmes and books that he reads. Wyng really gets me thinking and googling to find out the scientific truth of what he said.