I'm late to the game on this topic, but it's very timely for me in that I'm looking into getting an air source heat pump installed in my old (1855) small house. Both the federal and the provincial governments are offering grants of up to $10,000. I couldn't understand how they work, either, so I've visited one family to learn about their system, and I'm visiting another later today. I'm in climate area 5B, southern Ontario, so cold winters and hot summers.
Two other people around here who have heat pumps are thrilled with theirs and coincidentally both said that they spent only $200 on propane last winter. The kicker seems to be the electricity cost. This house is oil heated now, so I could use the current ducts in the cellar and ground floor, but there are no ducts or heat upstairs and no air conditioning at all. I imagine I'll get a mini-split in the small two-room upstairs. The person I've visited said that the only thing he'd do differently now is to have a one-to-one system, rather than the three-to-one ductless system he has.
I have a wood stove (replaced my old one a few years ago and wish I hadn't as it worked much better than the new one), but I doubt they'd permit that as the back-up heat source. We'll see. My fingers are crossed hoping that this will all work out.