Never been to Lemp Mansion myself (bit far from Somerset to be honest) but cold spots near staircases are something I've encountered locally and they're worth taking seriously rather than just writing off as drafts.
The thing is, staircases in old buildings are notorious for natural cold air movement - warm air rises, cold settles, there's usually gaps around skirting boards and under doors. So before jumping to conclusions I'd want to rule all that out first with a basic thermometer log over a few hours.
That said, if you noticed a localised drop that didn't move or spread the way a draft would, that's more interesting. Did anyone have a decent thermometer on them or were you going off feel? Because "feel" is genuinely unreliable, our bodies play tricks especially when we're already in that mindset of expecting something.
What were the conditions like outside that night? Would love to hear if anyone else picked up the same spot independently.