It depends on the current draw. I would guess that much below 40F or so they're really limited.
I have an outside temp sensor that transmits the temp and humidity. A set of 2 AAA's alkies runs about 2 years. It's worked fine down to -10 and lower.
On the other hand, I wouldn't expect them to give much light if you had, say, a PT Tec 40 or other light which would drain them dry in 2-4 hours.
There must be a temp current curve somewhere that shows what the current drop (or equivalent increase in internal resistance is) by temp......