In the cold, NiMH batteries, like the typical AA rechargeables, lose a good amount of voltage and longevity. My AA lights signal low voltage after a couple of miles. My winter commute is fairly short (4½ miles) so the longevity isn't a problem for me. But on longer rides I've had them shut down before the rated amount of time. Inside, after warming up, everything's hunky dory again.

It should be noted that the cold does not seem to have an effect on how long the charge lasts over the week. I don't have to charge any more often in the winter. It's just how long they can be outside before temporarily losing voltage.

Should you decide to go AA NiMH, there are no better chargers on the planet than those made by Maha. I own a Maha MH-C800S. Electrically, it functions as eight separate chargers. Thus, you can spot and replace weak individual cells, rather than having to guess, or replace all four, and one bad cell won't spoil the charging cycle for all of them. It has three modes: Fast, "soft", and conditioning.

IME, lithium-ion battery packs do not experience low-voltage or longevity problems in the cold. At least not at the temperatures we get around here. Our winters are generally in the teens and 20s with a week of single-digits.

The baseline of my experience is using a NiteRider TrailRat with proprietary NiMH several winters ago, six winters with DiNotte 200L-AA headlights and their 140R taillight, and three more recent winters of using proprietary lithium-ion battery packs in Magicshine headlights and a DiNotte 300R. I still use the 200L-AA lights as DRLs.