Generally, they can work anywhere in the continental US. (Assuming you live in the US.) If you're in northern NH, NY, VT, or Maine, you might want to keep your gas system as a backup. (New homes tend to have electric backup, but if you have an older home they just keep your furnace as backup.)

I have a 3000 sqft house in MA with a heat pump as my primary heat, and an electric strip as backup. The heat pump goes into the ductwork for most of the house. I generally haven't had problems. (It did have to be adjusted because it was the first time the installer put one in.) I have solar and usually get 1-2 large bills in January and February, and then March and April are very cheap, if I get a bill at all. My "large" January and February are comparable to what I'd spend on conventional heat.

Last weekend we had a "once in a century" cold snap down to -4. Most of the house was at temp, but one room fell to the high 50s. From what I've heard, plenty of people with conventional heat had far worse issues than a chilly room.