We had those in NZ (also known as AirCon in Australia). Ok until it got too cold and would have to have a 'defrost' cycle for 15 minutes oh or go completely when the power went (5 times in 2 years, reminded me of the 70's). Anyhoo...
We also had a fire and electric heaters, waking up in 12 degrees with a numb head isn't great fun in the winter, above all else sort out insulation before heating.
The house we were in, great location, but built like a shed - back in the UK with similar temps and I barely have to have the heating on because our insulation is so good. Yeah it's not as old as the one you're dealing with (very envious btw) but I would try and figure out your insulation first (there must be options even for old buildings) otherwise you'll be throwing cash out the window.
Oh yeah, and insulation.