Assuming that the Model S uses the HV pack and a DC/DC to power the 12 V bus all of the time (like the Roadster), it would make sense that parking the car overnight in the cold would cause issues.
All other EVs that I know of shut off the battery contactors when the car is keyed off, and rely on a 12 V SLI battery (usually lead-acid) to support the vehicle when the power is off. The roadster did not do this, which is explained in Tesla's BMS documentation [1]. This means that any quiescent current consumed by the 12 V system will drain the main battery pack.
All other EVs that I know of shut off the battery contactors when the car is keyed off, and rely on a 12 V SLI battery (usually lead-acid) to support the vehicle when the power is off. The roadster did not do this, which is explained in Tesla's BMS documentation [1]. This means that any quiescent current consumed by the 12 V system will drain the main battery pack.
[1] http://webarchive.teslamotors.com/display_data/TeslaRoadster...