You can wire a heat pump with 3 wires to either heat or cool, but not at the same time. If you wired it to cool in the summer you would have to rewire it in the winter to make it heat. With only 3 wires you would not have a defrost in the winter time nor any monitoring controls.
OK, "IF" your heat pump has a defrost board that does require being energized all the time, you can get away with wiring just the contactor hot lead, the reversing valve hot lead and the common.
With that configuration, only "IF" a continuous hot lead is "NOT" required by the defrost control, your heat pump will operate both heating and cooling but will not energize the aux. heaters during defrost.
Now..."IF" your heat pump happens to be a Rheem/Ruud product that requires constant energizing of the defrost board, you can also jumper the reversing valve control lead to the "hot" lead on the defrost board and it will still operate.