P.S. Obviously any chemical battery (though presumably not nuclear) will eventually die out if you lower temperature enough. There was a guy describing experiences of riding on S Pole, but I could not find his writing online recently. He had to regrease his bike completely, because the regular grease solidified, and he might have needed to get rid of some plastics. In any case, I aim at temps down to -30C, though recently we barely get to -20C. The NiMH have been near to useless below -15C or so, no matter what brand. However, the lithium technologies pushed down the utility to lower temp. In my main power station on the bike, I even use some less common lithium batteries that perform better at low temp than the popular.
If you tested them in the freezer, that is a good test. The Ladda batteries that I spoke positively on are white in color, but they have had brown ones and now have some gray ones. Each has different chemistry.
Arctic explorers need to use mechanical watches, watches with batteries do not work for them in cold.
Riding a bike at the S Pole, that sounds a little rough. Rohloff has suggestions for different lube oil in their hubs in really cold weather but if it is colder than about 20 (F), I do not use a bike.
If this is strictly for winter use on a bike for lighting, perhaps skip battery power completely and use dynohub lighting?
About 45 years ago I needed to use some battery powered flashlights in below zero (F) conditions. I found Rayovac Heavy Duty to be best, they were cheaper than alkaline batteries at that time. But I do not even know if you can buy non-alkaline disposable batteries any more.
Maybe a battery store like Batteries Plus would have some suggestions?