Ladda batteries die in the cold and got restricted to indoor use in my household. Eneloops struggle in the cold, but are still usable.
I think it depends on how you define cold. I do not like hot weather for bike touring, most of my tours were planned to be in places that are cooler than average. But I find that in the temp range of 40s or upper 30s (F) they work fine.
I use Ladda AA (white color) batteries in my GPS, that works fine in temps from the teens (F). But for high flow rate usage like a flashlight you might need disposables in really cold weather. I have used that to keep track of my route for cross country skiing.
On the other hand I tried to use my camera on Monday outside, temp in the upper teens (F) and although the Lithium Ion battery had been charged up the night before, it only had one yellow bar for power. Indoors where it was warm, that battery showed fully charged again.
When someone says cold, I really have no clue how to interpret that, as I grew up in Minneapolis. To me if you spit and the spit breaks when it hits the ground, that is how you know it is cold out.
Now I live down south in southern Wisconsin where temps like the photo are rare, but occur. It is supposed to get down to minus 8 (F) on Fri night here.