While disinfection by chlorine, bromine or iodine IS temperature dependent (lower temps require higher concentrations abd/or more time to be effective), in this case, chemical bonds aren't being broken/formed with other molecules (higher temp molecules are more reactive), but with UV photons.
The article details how UV photons makes thymine-thymine bonds in DNA rendering a virus, bacteria, etc, sterile - unable to reproduce/divide. That process is not very dependent on temperature.
Also, you're using lithium batteries (you pretty much have to in all the units), and they are much better at low temperatures than alkaline or nicads that we have more day-to-day experience with. That said, all batteries put out less current when (1) cold and (2) partially used. If you've got partially used batteries and they don't start/complete a cycle when cold, warm them up. My estimate - not a problem to 0C and 2/3s used, but I haven't tested that.
The batteries WILL, kind of, work "as long" at cold temps. The issue is if they can put out the 1 amp needed for the UV lamp. Even when cold, you'll get almost all the electrons out of a battery that you would at 20C, but maybe not at the current required by the device.
Edited to add my estimate for your original question: I suspect you are okay to 0F OR 2/3's used. i.e. it will probably work to 0F with new batteries. Or with largely drained batteries if warmed. But maybe not both. But if you're going to sterilize water in the next hour, it would be easy enough to put it in a shirt pocket under your jacket.
Edited to correct "breaks bonds" to "makes bonds". Thanks to Bill for catching that.