Common sense is not actually a reliable measure of truth. Can you provide some physical reason why this would be dangerous? Because I can’t think of any.
I have, as I noted above, Central Pain Syndrome. What that means is that I have hyperalgesia and alodynia caused by overactive nerves in the CNS. Things that are merely uncomfortable for the average person cause pain for me, and painful things are exaggerated (hyperalgesia). Non-painful things cause pain (alodynia). For example, when the hair stylist sprays the room-temperature water in her spray bottle to wet my hair for a haircut, the spray that hits my skin feels like fire burning my skin. A breeze from a fan feels like sandpaper removing my skin. If your “common sense” held, for me water sprays and fans would be dangerous. But we know they’re not. We know that not everything that hurts is dangerous. So what about holding something cold in your mouth and breathing through your nose is dangerous?