Responding to this and more generally to everyone mentioning insulation: I'm not saying that insulation is irrelevant, but when I say it fades out at low temps, I mean that if I put my hand over the forced-air duct it feels at best maybe a tiny bit warmer than the ambient air. (Which together with the forced-air circulation makes the room feel even colder, even if the temp is technically going up, but that's more a complaint about forced air, not heat pumps.) Insulation problems would mean I'm running it more and I'm paying more to heat the place than I might with better insulation. But insulation problems aren't what's causing the emitted air to feel cold.

Also, as noted, I'm sure part of it is that they gave me a heat pump that's rated to 5°C or whatever instead of -15. Probably because they expect that everyone around here has a backup heating system, and it doesn't get Sweden-cold (or Chicago-cold, for that matter) in this area. Cool cool, but that just reinforces the message that heat pumps can't hack it and if you're buying a heat pump system you really need to also buy a second system—which may not be entirely true but there's other people on this very thread with a kind of dismissive "everyone knows" attitude regarding backup heating that fundamentally undermines the original message (which was my whole point).

it isn't insulation.

It depends primarily on your electricity and methane prices. In Ontario, Canada, electricity is cheap enough that heat pumps are cheaper than methane on all but the very coldest days, even if your home insulation is older than 1980 standards.