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!).