Did old Manhattan mansions have insulation in the walls?

Depends upon how old the structure is.

If it had knob and tube wiring for electricity then the walls probably were not insulated, to allow heat to disapate from the wires.

Fascinating, thank you.

I’m not quite sure about what you qualify as old, but european based NY brick or brownstone construction was not isolated apart from wall thickness. Several reasons to this, the main one (since isolation materials were not readily available) being a fundamental difference in heating “philososphy”. today we demand equal temperature throughout the dwelling, with eventual warmer areas, in the recent past (up to circum 1950, 1930 in heavy urban constructions) heating was a “central point” idea, going back to the open fire; getting close to the source was warmer. Other non critical parts were cooler or cold (unheated)
I don’t have the info for NY but mean temperature in high quality lodging in Paris, France 1935 was 15°C (year around). This clearly underlines a “warm area” close to a stove in the living room (the term takes sense here), and near glacial corridors and bedrooms. Individual cheminees could be present in rooms (subject to presence of domestic personnel, carrying wood or coal, lighting and maintaining fires, cleaning ashes)

Also fascinating. Boy, if anyone ever makes the mistake of bringing up this subject (which is unlikely) I’ll be ready for 'em!