“But, if I understand it correctly, the heat pumps that are good for really cold weather are not the variable speed ones.”
I had to do some research.
To be rated as CCHP, Cold Climate Heat Pump, the unit must maintain down to 5 degrees F the same efficiency as at 47 degrees F and work efficiently down to -15.
These units commonly are variable speed.
Perhaps my research is old (3.5 years ago when I installed mine). But back then the only heat pumps that went that cold were either single stage or dual stage, not practically infinite stages. Which is fine if you're main goal is to fight bitter cold (live up north). But if your main goal is to fight heat (live in the south) then you have the luxury of the heat pump not having to work hard to find heat from the air it draws in (would like it to have various options of low or lower speed).