The Haier says it will make a dozen small cubes in 6 minutes, and I think I saw an advertised amperage draw of 4.4a. Assuming those numbers are accurate:
4.4 x .1 hour (6 minutes: gives "small" cubes") = .44 amp-hours.
4.4 x .15 hr (9 minutes: gives "medium" cubes) = .66 amp-hours.
4.4 x .5 hr (12 minutes: gives "large" cubes) = .88 amp-hours.
Of course, the Haier is AC, so you'll need an inverter
and will lose some efficiency there, so if you want to be extremely conservative and let the theoretical inverter
waste 20%, you can figure a bit more than one amp hour of battery
capacity for 12 ice cubes."
$175 or so for the machine, I don't know how much for the inverter. But it'll do-her.
If all you want is to cool a couple of drinks occasionally, this would be much cheaper than installing refrigeration
Others: please feel free to point out blunders in my math.