When you say "super low power" how long do you want the device to operate from a single battery charge?
My guess is that the amount of energy used by any motor that can do what you need, even if running for a brief amount of time, will be 1 or 2 orders of magnitude greater than the energy needed by the microprocessor so I doubt if being super-abstemious with the MCU is important.
Have a look at Nick Gammon's low-power tutorial.
Really, you need to hook up a suitable motor and measure the energy it uses while doing the job you require. Then you can figure out the appropriate size of battery.
If you are thinking of using a lead-acid battery you should be aware that they do not like being left partially discharged for more than a few days. Maybe you could use a solar panel to keep the battery topped up.
If the application just requires something to open and close then maybe a servo would be convenient as it has the motor and the control electronics in a convenient package. If necessary you can get your Arduino to shut off power to the servo when it does not need to move.
...R