Our house is from 1900, so the kitchen was added at a later date. We have nothing but a crawl space under the kitchen that needs insulation, but that never seems to get done for some reason.
Beau blows a fan in there to keep air moving, which helps to some degree. We’re going to be VERY cold this upcoming week and either no snow, or a LOT...they haven’t decided, yet. ;)
Our fridge water line will freeze, as will the kitchen sink pipes, so I do the same as you with the dripping water, which the cats find fascinating...
I realized the fridge line is actually for an ice maker, so when it gets cold, I’ll just make me some ice overnight to keep that thing moving.
Fortunately, I really only have to worry about a few nights. Pipes tend to freeze when it’s 20 or below for 6 straight hours or more, and apparently usually don’t if those conditions aren’t met.