Every heat pump is an air conditioner, not every air conditioner is a heat pump. They require a reversing valve to function both ways.
The furnace doesn't need to change. I have a nat gas furnace with an electric heat pump. You can also do electric heat pump with an electric air handler. There are plenty of combos.
That said, every year I run the numbers and despite my heat pump being ~300% efficient my 95% efficient nat gas furnace is still cheaper to operate (based on the cost of each energy source). I'd LOVE to go solar and operate as close to 100% electric as possible but with my old growth trees and shitty house orientation I wouldn't even break-even in the lifetime of the panels. :(