I've just dug out the specifications of one of our units, a multi-split which powers two indoor units.
Input power for cooling varies between 0.18kW and 0.6kW, while cooling capacity ranges from 0.75kW to 2.4kW.
Input power for heating varies between 0.17kW and 1.02kW, with heating capacity ranging from 0.7kW to 3.6kW.
So, on these figures it uses less electricity when cooling, which is probably more to do with the smaller temperature differentials rather than anything inherent in the mechanical process: it is, after all, the same equipment - just operating in reverse.
However, whether it's heating or cooling the effect is much greater than the electricity it consumes: the ratio is the co-efficient of performance. So, if it's running at full tilt in cooling mode it converts 0.6kW of electricity into 2.4kW of cooling effect, and in heat mode it turns 1.02kW of electricity into 3.6kW of warmth. This is the reason we're all being encouraged to switch to heat pumps for heating - not only does it enable a switch from fossil fuels to electricity and therefore renewables once the grid is properly decarbonised for domestic heating, they're just much more efficient.
We power ours for cooling in the summer with a 6kW photovoltaic solar array and 9.5kWh battery: yesterday it kept the house cool all day, and three bedrooms airconditioned through the night, without drawing anything from the grid. The only heat AC adds to the environment, as OP would have, is the small amount of heat the plant itself generates. Most of the 'heat' you can feel near one of these things is not additional generation, but heat being displaced from the room. When running in heating mode, they actually blow cold air out.