For teslas, a plugged in car is a happy car.
To answer your question, it depends a little bit on the specific model you have and its BMS firmware, but in general, there are 3 different charging states the car can be in:
1) “voltage mode”: In this mode, the car’s onboard AC -> DC charger is enabled and is providing power to the vehicle (eg to heat the battery), but the actual contactors to the HV battery itself are open/not connected. In this mode, the battery does not charge.
2) “power mode”: This is the normal AC charging mode. In this mode, the HV battery is being charged by the car’s inverter/charger at a specified voltage and current.
3) “DC fast charge mode”: in this mode, the onboard charger and is bypassed, and the chargeport is directly connected to the HV battery. The external charger manages the DC voltage and current going to the battery.
When it’s cold out and you leave your car plugged in to AC power, its BMS will switch between the first two modes automatically. If, for example, your battery is charged to your set level and you enable the car’s HVAC, it will use “shore power” (via “voltage mode”) to run the HVAC and will not need to draw from the battery.