I commuted all last winter on my Level.2. I stored it in the garage overnight. Left outside all day. Some days were pretty cold, in the 20s. My commute is only 2 miles, so I can handle just about any cold for that distance. I did take the car when it got below 20 °F.
The cold will cause the battery voltage to drop, although it will discharge just fine down to -25 °F or so. You will have less apparent capacity because of the voltage drop though.
In your situation, yes, I would bring the battery in during your shift and keep it room temperature inside. It's very easy to remove the battery from a Level.2. Then, when you go outside it will retain SOME of that warmth (and voltage) through discharging.
Consider getting a 2nd charger to keep at work, as a back-up plan.
What you'll find to be more of an issue is keeping your hands & feet warm enough and keeping the cold wind from making your eyes water uncontrollably. For the hands, I wear
thin fleece Head running gloves (from Costco) inside of ski mittens when it's really cold out, and wear the right boots on the flat pedals. (you can fit bigger pedals if needed) I'm looking at heated mittens for this winter; good ones are down to $80 on Amazon.
For the eyes, I bought a pair of
Wynd glasses from Amazon with the yellow lenses. They are just great. They fog when you come to a stop, but clear up quickly once you start rolling again. They have a foam "gasket" that fits against your face with just enough openings to let air in to defog them. Only downside to them is that they completely block peripheral vision, so make sure you have a mirror either on your helmet or on your bike.
The jacket will be no problem; I recommend something with a high neck or a scarf. If you're working at all, overheating will be more of an issue than being cold.
I got a set of simple nylon overpants to go over my work pants. These serve a dual purpose to keep me warmer and keep road dirt & salt off of my nice pants. You might need more than just thin ones though, since you're going 5X as far.
Windchill is something to factor in too. Going above PAS1 was not helpful during the winter. It just made the windchill worse. I alternated between PAS1 and PAS0. (to make more of my own heat) At PAS1, a 20 mile daily commute will be no problem; charge every other day, instead of every 3rd day in the summertime.
More on my Level.2 ownership and optimization here:
https://ebikesforum.com/threads/aventon-level-2-review-thread.3764/