@garlock
I sounds like exactly his situation. "
plugged in the level 1 charger the next morning ..." He left the car unplugged all night in extreme cold conditions. The battery *really* doesn't like being below freezing, and doesn't work as well below about 45 degrees or so.
I would suggest plugging in the level 2 charger, get in and start the car, turn the heater on to about 75 degrees, turn the car OFF, get out and use the 'battery conditioning' feature on the fob (lock the doors then hold the bottom button down for about 4 seconds to start battery conditioning). This will run the battery warmer for 20 minutes. Do it a second time, for another 20 minutes. That should warm the battery up to above 40 degrees (hopefully). If not, get back in the car after the second 'conditioning cycle', turn the car on again (the 'remote start' can only be used twice - then you have to start the car). Get out and run the 'battery conditioning' another time or two.
If that fixes the problem THIS TIME, it sounds like you should simply leave the car plugged in over night so that the car keeps the battery warm. If the car is plugged in, it will keep the battery from getting too cold. And put a 14 gauge or 12 gauge (i.e., 'heavy duty') 25-foot extension cord in the trunk along with the 120V charger if you are going to leave the car parked in 0 or 5 degree weather for hours. And always 'remote start' ('battery condition') your car for 20 minutes before leaving home to warm the battery.
There is a 'trick' to safely charge your vehicle in public without losing your personal charger.
(a) lower the driver's window just enough to fit the extension cord and charging cord from EVSE through the crack.
(b) Run the extension cord through the crack, and loop it through the steering wheel several times so it can't be pulled out of the car. Ditto the charging cable (side with the J1772 plug), so that IT can't be pulled out of the car.
(c) plug the EVSE into the extension cord, leave it inside the car. Plug the J1772 plug into the car, and walk away (after locking the car and checking that the green light is blinking).
This way, nobody can steal the ext cord or the EVSE, since it is firmly wrapped thru the steering wheel.