Before pursuing it, look around and see if others have outdoor compressor units and if not, check with the homeowner's association to see they would allow you to have one installed. If no one else has done this, I wouldn't be optimistic about getting permission to be the first. Also, note that such equipment needs 220V wiring and having the wiring added for that may also make additional changes (wall mounted conduit) to the outside appearance.

Good advice, thank you

Also, with the frigid temps we had this winter (and others) I would consider leaving the electric baseboard as a back-up. The heat pumps aren't great for really cold weather, but the mini-splits apparently are efficient down to a lower temp than other heat pumps.
I had some questions about this exact thing this winter and there was a great discussion you might want to read here: https://www.houzz.com/discussions/6212919/will-it-harm-my-heat-pump-to-turn-it-off