I would not want mini-splits in a house in the north east. it gets cold and you need to heat evenly. Plus you'd need them in every room incl. bathrooms so the pipework would be nuts!

Mini-splits are not uncommon for cooling in the summer, but then again you only need them in the main living areas and bedrooms.

Tons and tons of people have mini splits in the northeast!

You don’t actually need it in every single room. A lot of rooms, you can get away with like radiant floor heating or electric baseboards.

If you didn't have an actual heat source in your bathroom, it'd almost certainly freeze when it's <20F out. I'd also imagine that most of the mini-splits you see around the Boston area are for cooling and probably aren't designed for heating in the winter (most HVAC companies tend to spec the cheapest of the cheap condensers for the outside unless you are specific about heating). I actually have a Trane/Mitsubishi ductless mini split and it struggles when it's cold out (eg 30's) and will use AUX (resistive) heat (it's in a garage and is for cooling in the summer!).

A baseboard heater or something like a cadet heater are more than enough to keep a bathroom warm