The Mitsubishi Hyper Heating units turn themselves off to self-protect at about -20F, but automatically re-start when they get up to temp. The lowest tested-rated output is at -25C/-13F, but they're still putting out decent heat at lower temps until the controls self-stops. If that's a show-stopper, move on to the Fujitsu units.
The
Fujitsu xxRLS2H series just keeps on chugging no matter how cold it gets, but the heat of output isn't tested or guaranteed below -15F. Second hand beta from folks in the Adirondacks of NY say the the RLS2 (not -H) series is still putting out a decent amount of heat at -20F. The Fujitsu AOU-15RLS2 puts out about 17-18K @ -5F, and is probably a better choice than the 1-ton. It draws draws 6.1A @ 230V in heating mode, and even a 2-ton will usually be under 10A.
I wasn't too far off with the -5F design temp, eyeballing the
WeatherSpark dataset.
So new napkin math:
Walls, 8' x 100' for 800 square feet, for U0.12 x 800' x 75F= 7296 BTU/hr
Windows 90' @ U0.5 (unless they're low-E, argon filled or something) for U 0.5 x 90 x 75'= 3375 BTU/hr
Same 660' attic for 3960 BTU/hr
Same crummy leaky door at 1000 BTU/hr
Same 2000 BTU for floor loss fudge factors & random air leakage.
Adds up to 17631.
If you wanted to invest in low-E storm windows (the Larsen low-E storms sold through box stores are on the order of a couple hundred per, so it's not ultra-cheap, but it the payback is quicker than cheap clear-glass storms- should be under 5 years at the ultilty pricing & efficiencies we've been descussing.) A low-E storm enhances a U0.5 window into U0.28-U0.3 performance, peeling about 1400BTU/hr off the total.
Any air-sealing you can do (including the holes for the pellet stove venting) can knock another 500-1000BTU/hr off it at VERY low cost, if you're the type of DIYer who can take it seriously. A ~20 square foot solid wood door has a U-factor of about 0.5, so with decent weatherstripping it would come in at 750 BTU/hr, not 1000, and that's probably not the biggest air leak in the place. The closed in porch probably takes 500-1000 BTU/hr off the whole thing if it's reasonably tight.
You can take off another 250 BTU/hr per sleeping human, and another 150 for the refrigerator (unless it's on the closed-in porch, or IS the closed-in porch.
).
The better than random guesstimate is you're looking at something on the order of ~15,000 BTU/hr @ -5F. A 1 ton like the -12RLS2H or -FE12NA would do, if you don't mind waking up to a house that's a bit under 65F on the very coldest nights, or want to install a 1500W (5000 BTU/hr) space heater or radiant cove-heater to cover the shortfall for when it's REALLY really cold. Cove heaters are cheap and provide very comfortable heat (way more comfortable than finned baseboards of similar cost), but if controlled via thermostat you'd want to set it for something like 65F when the mini-split is set much higher, so that it only runs when the mini-split really CAN'T keep up, (which should be less than 5% of the time even with a 1-ton.) Heat provided by the mini-split uses only about half the power of the cove heater even at -15F outdoor temps, and only 1/4 the power at +40F, so any resistance backup heat should be used only when needed. But the -15RLS2H or -FE18NA is probably going to be the better choices here. Both put out ~15,000BTU/hr at -15F outdoor temps, but 17-18K @ -5F, so they should handle the whole load most years, if not quite keep up during the cold-snap of the century.
I think that's an -FE18NA compressor on the side of that green house in the picture. It's heating & cooling a whole ~1400' multi-story superinsulated house with some margin in a climate comparable to yours (Cambridge, NY), but the R-values are 3-4x those of your cottage.