Dear Tina -
Hmmm - if cold water was a trauma, how about all the people who eat ice cream, popsicles, and other frozen things? I imagine if you ate a raw ice cube and it stuck to the lining, that could be bad, just like licking an ice cube sticks it to your tongue skin. So that I could see. Maybe he's just talking about not ingesting ice.
I.e. skin would care if it got frozen. I think as long as you don't freeze the skin, that it does its normal skin-functions. Just like we go out in snow, and we're OK, but it's not wise to press your hand down on ice for long periods of time.
That would be my guess!