I'm a big fan of lithium ion batteries but was not aware that they may be useless at -10 degrees celsius (14F) and seriously compromised when it approaches freezing as shown in this chart https://www.google.com/search?q=Lith...A3V4Wd6zo2M%3A or figure #11 in this article Willkommen bei BaSyTec. It's not the fault of the light. We all love having bright lights that have a long run time between discharges and LED/Li-ion battery combination provides that for the time of year that most people ride.

You might do better by buying an inexpensive 1000 lumen XML-T6 LED flashlight that uses both 18650 Li-ion batteries or three AAA alkaline disposable batteries. In really cold weather it will still give you an excellent output with alkaline batteries and when it is warmer switch to rechargeable batteries.
Like this - two (real output 1000 lumen) flashlights for $8 USA 2PCS Zoomable CREE XML T6 LED 5000LM 3-Mode 18650battery Flashlight Lamp | eBay the battery case for using 3 AAA batteries $1.48 for five of them 5X Plastic Flashlight Cylindrical Holder Case Battery 18650 Black Box For 3 AAA | eBay
and a really good mounting clip for $1 360 Degree Cycling Bicycle Bike Mount Holder for LED Flashlight Torch Clip Clamp | eBay from China