It's a simple idea, but it's not quite that simple.

When it gets to be around freezing outside, you have to deal with frost buildup on the outdoor unit.

And as temperatures fall, output and efficiency generally falls. So you need an oversized unit to heat your house on the coldest days, but an oversized unit isn't great the rest of the year.

Historically, heat pumps were only good if it never got down below freezing. Now, modern cold- climate heat pumps are efficient well below freezing and Mitsubishi's models advertise that they deliver 100% of their output down to -23F/-30C. Between adding variable inverters, better defrosting, etc they've come a really long way in the past decade.