And small, unpressurized airplanes don't need cooling. The air outside
is plenty cold. For heat, there's lots to be had from the exhaust or
oil with a simple heat exchanger.

In a pressurized airplane, I don't think the vortex tube would work. I
don't think you can exhaust the cold side into the cabin and the hot
side overboard, so I think you're back to conventional AC.