Thank you all very much for your ideas, there is a lot to think about!
@dick_freebird: I will consider dry ice definitely, too!
Ordinary freezer compressor kicking in was certainly something I didn't think of. I see you all recommend something else than messing around with inverter.
I should take some time to study more about peltier elements and consult someone on the solutions.
I took a look at those elements on Ebay and in local shops and found out that there is a really huge price range... as I'd like to do the project on lowest possible budget, I can consider only cheaper ones.
Here, in the edge of Northern-Europe, summers rarely exceed 23 degrees C. Ice cream should be kept at -17...-20C which may be considerable range.
I found what seems to be a trustworthy graph of 12V peltier performance here:
http://www.heatsink-guide.com/peltier.htm
As much as I understand those graphs, I could tell it might even come into consideration. But the Delta-T given there isn't really difference between outside air temp and ice cream temp inside, is it? How should I find Delta-T I need?
I think I could get kind of low wattage peltiers, even if I'd add 25% efficiency reserve + container heat loss, which can be calculated.
Best,
Andry