I also live in a climate that experiences extreme low temperatures in the winter. I've rarely had any problems with dash cams booting up in cold weather but one of my Mobius cams (first gen) sometimes won't boot up when it gets too cold. The LED lights up, blinks three times to show that the super-caps are properly powered up but then nothing happens. The solution is to simply leave the camera plugged in for anywhere from 30-60 seconds, unplug the camera from the power source and then plug it back in. Once the internal components begin to heat up a bit from being plugged in the camera will boot up as it normally should. This technique works every time.
Of course, this is different than a camera that keeps rebooting over and over. I would suggest an experiment you can try as part of your troubleshooting. The A129 Pro should have a boot delay in the menu. Set the delay to the longest time that it will allow for and see if anything changes. This "may" reduce the number of times that camera boots until it's components reach their minimum temperature specs to function properly.
Another experiment (if you haven't hard wired the camera) is to unplug it after it has had power for a few seconds and then plug it back in. If it is hard wired, try turning it off and then it on again after waiting a brief period.
See if any of this has an effect on the problem.
