>> And so, what could be the ideal power supply for outdoors use?
Are you already powering your mount, dew heaters and the camera cooler from a 12V supply? If so, the same supply should also work for the ASIAIR.
From what I can tell, the 12V-5V converter uses a step-down "buck converter," so it should provide a constant 5V to the ASIAIR even when the battery voltage has fallen substantially (even down to about 9V). The ASIAIR, when used with the 12V-5V converter that comes with it, should be very forgiving of the power supply that you use.
Just connect the input (12V) end of the 12V-5V converter that comes with the ASIAIR to the common 12V source.
I have not measured how much the ASIAIR draws when it is autoguiding.
When the ASIAIR is idle, it draws an average of about 0.35A.
When the ASIAIR is constantly downloading images at a high rate in the Focus mode from an ASI071-Pro, the ASIAIR's power converter draws a peak of a little under 0.5A from a 12V source. If you are using a 20Ah battery, it would last over 40 hours if the battery is only used for providing power to the ASIAIR in focus mode.
Compare the ASIAIR power consumption with the cooler that is in the ASI071-Pro, which draws almost 0.9A when running at 70%.
Clear skies,
Chen