Never been to Waverly Hills myself but cold spot reports from that staircase go back decades in the literature. What's interesting to me is whether anyone's actually logged the temperature differential properly rather than just going by feel - human perception of cold is notoriously unreliable in already-anxious states.
That said I don't dismiss it. There's a reasonable body of work suggesting that certain kinds of energy release - and I'm including the kind associated with SHC precursor conditions here, which is my main area - can produce localised thermal anomalies that go both directions. Hot and cold. Most people only write up the dramatic ones.
What were the conditions like that night? Time, humidity, whether the building had been open long before your group went in. All relevant. If you've got any actual readings from a thermal camera or even just a basic infrared thermometer I'd genuinely like to see the numbers rather than the anecdotes. Not being dismissive, just want something to work with.