[DickR]

A house that old likely leaks a lot of cold air in winter, and wind-driven rain often gets behind the siding and past whatever flashing may have been done around the windows. But, with a lot of air leakage, the house would be very tolerant of water leaks, as the air movement would dry out the walls quickly with no real harm done.

If you add insulation to the walls, such as by blowing cellulose in from the outside, and you do nothing to improve the exterior regarding water leaking in, then you can create a problem in the course of solving another. Insulation in the walls can retard drying, with the possibility of rot and mold development. This isn't a given, but a risk to consider. There are plenty of more recently built houses that have such problems for the same reason, often undetected until the wall is opened for some reason.

This region is not particularly rainy, as would be, say, the Pacific Northwest. Here we typically have plenty of time between rain events for things to dry out. Still, given that the house is that old, if I were thinking about adding insulation, then I'd be thinking about also removing the siding, adding a housewrap or asphalt felt, and putting on new siding, unless this already has been done. Besides adding protection for the new insulation, you would be tightening up the house dramatically, making it much more comfortable in the course of reducing the heating bill.

Edit: who says NH electric cost is low? I'm on NH Electric Coop, and I think at present it's around 18 cents/KWH. Not cheap.