Do you have a citation for that? I was under the impression that was an "old wives tale". Human's often face huge temperature swings in winter.
In fact we go out of our way to experience these swings with saunas and cold plunges. I have put this up in the same category of "wet hair gives you pneumonia", but I am open to learning one way or another.
To be fair - cold air hit (I'm talking about big gaps betweet temperatures) is pretty bad for you.
Ideally you don't want the temperature in a room to be (immediately) lower than T-5°C or so.