RMR battery life in subzero temperatures

I recently started carrying an RMR-equipped G19, and I had a concern. If I have to repeatedly leave the gun+optic in the car overnight in subzero temperatures, will the battery life be dramatically affected? Let’s assume normal brightness (setting 5 or 6) and quality battery (Duracell, Energizer, Sony).

A little background: I work in a hospital, which in IL is a GFZ. I wear scrubs, so “concealed is concealed” doesn’t apply even if I wanted to be a felon. So, I have to leave my EDC in the car overnight 3x a week. It seems that every year we get a week or so of temps close to or below 0 F. I plan to change RMR batteries yearly on my birthday, but would carrying it to work during those brutal winter weeks cause the battery to die sooner than 1 year?

(Bonus question, will it affect my X300 battery life as well?)

Not sure about your specific question, but I had to replace my battery yesterday so just as an FYI, mine jumps between the second and third highest settings (6 & 7 I think?) depending on what I'm doing and I'm getting a pretty consistent eight months of use.

Assuming you are using lithium batteries you should be OK, they are rated to 40 below and work much better in cold temps than alkaline batteries.