When the GPS tracker is not moving, it consumes very little energy. The battery can last up to 1 year if it's not moved. Every 24 hours it wakes up to report its status. It also wakes up to report certain battery conditions.
In cold weather modern lithium ion batteries operate poorly. The ions starts to move slowly and the battery loses power. Automile uses lithium ion which is the most common battery in the industry. Using led- or nickel-cadmium, which could work better in cold conditions, is not environmentally friendly and also has other issues. If you want to know exactly what happens in a battery in cold conditions, you can read more here.
Automile has tested its GPS trackers with the built-in battery down to 14℉ (-10C), but at temperatures below 59℉ (15C), the battery will start to be affected. Under 32℉ (0C) it will operate much worse, and battery life will be shorter. The device can be used down to -22℉ (-30C) when it is wired to an external power source. Lithium batteries work optimally around 59℉ - 77℉ (15C - 25C).
When you use a GPS tracker in cold conditions, especially under 32℉(0C), the battery life length will be shorter. Every hour the battery will discharge in small amounts, and eventually you will see in the app that the battery level declines faster than normal. This applies to all modern battery powered products, not just Automile's.
It's difficult to tell exactly how long the battery life length will be under certain conditions because it's very dependent on exact temperature, update settings, and what you are monitoring.