I've been looking at the new split type AC/ Heat pump units. A 18,000/ 9,000 BTU dual (two inside units driven by one outside unit) head one is about $3,000 before installation. You can do most of the work yourself, but it's mandatory a licensed AC person fire it off the first time. (At least here in Maine....also , there is a bit of a rebate. It was $800, but that one ran out of funding. Now it's looking like $600. Check with your electric company).
Yes, the SEER rating on the new units is very impressive, but perhaps not quite as good as it seems on the surface. They are variable speed compressors and the rating is calculated at the slowest speed, just before the room "is satisfied". Under full load at full speed the rating is lower, BUT... the bottom line is,: The new ones ARE much more efficient than the ones of just 5 or 6 years ago, even if the numbers aren't 100% accurate.
I'm told the new ones are better at getting heat at lower outside temps..... even down to 10 degrees or thereabout. They are less efficient at making heat as the temp drops but still better than an element type electric heater. I do not know if or how they tell you "It's too cold outside to make heat".