I wonder if the cold weather issue would persist if a cold specific battery was used. There are some lithium ion 18650 with less capacity designed for colder weather use.
I've tested it with all kinds of batteries, from low drain to high drain. The battery doesn't seem to make any difference. It's the driver, it doesn't like the cold on H1. Note, the problem doesn't happen all the time, and once the light is warmed up (just takes a couple of seconds on H2), it goes away completely. So, while it's an annoying problem, it's not a game-stopper.
Since Zebralight has stopped shipping to anywhere other than the US, it's probably going to only affect Alaskan people. :ironic: