Well, it did feel "colder" than a cold winter day of, say, -25 C and wind outside, but I don't recall it hurting as such.

Then again, I didn't do deep breathing. I'd guess diaphragmatic breathing would've probably hurt in some way.

Overall the impression was a kind an inverse sauna if you know what I mean. In my experience taking deep breaths at the top bench of a dry and hot sauna stings, so the breathing naturally adapts to this.