Can a 12v power cord run your car battery down?

[PastTense]

Note your vehicle could well have other devices drawing current so there could well be a cumulative problem:

Most vehicles draw some battery current when the key is off, thanks to the clock and the internal memory of engine computers, body-control modules and radio presets.

How To Diagnose a Dead Car Battery

But this articles definitely mentions as you thought:

Unplug any power-draining cables from the lighter socket, such as a cellphone charger or GPS.

[scr4]

…and unplug stuff from the ODB2 port too. I once ran the battery down with an ODB2 Bluetooth dongle.

[Thudlow_Boink]

I have a car charger with an LED that I used to keep plugged in most of the time. I thought, like you, that it only drew a negligible amount of power when no devices were actually plugged into it. Then I had to replace the car battery after just under 4 years, which is less than I thought it ought to have lasted. I still don’t know for sure whether leaving charger plugged in shortened its life, but to be safe I now leave it unplugged.

[Northern_Piper]

@74westy

I’m pretty sure a battery can freeze at higher temperatures if it’s run down.

That may have been a contributing factor. Plus, it was a cold snap of -30 for about a week.

[Xema]

@Northern_Piper

… it was a cold snap of -30 for about a week.

Duration of extreme cold shouldn’t matter much - battery would easily reach ambient temperature overnight.

And while it will almost certainly destroyed by freezing, it isn’t the cold that is responsible for draining the battery. That had to happen otherwise, allowing the battery to freeze at this abnormally high temperature.

[Khendrask]

Seriously, the LED on a charger isn’t going to drain your starting battery in 3 months never mind 4 days.
If it did, then the memory on the stereo, and the standby power for the car’s computer would drain it as well.
Things that do drain a battery in a couple of days are large loads, like lights left on (under hood lights are evil for this, as are cargo area toggle lights.

[scr4]

@Khendrask

Seriously, the LED on a charger isn’t going to drain your starting battery in 3 months never mind 4 days.

It’s not the LED itself. The LED is telling you that the phone adapter is receiving power. Phone adapters are voltage regulators, and they consume some power even when there is nothing connected to its output. The amount depends on the adapter design, it may be negligible for some adapters but it may be tens of milliamps on some. 20 mA x 4 days is 2 amp-hours, which is non-negligible fraction of a car battery capacity. It shouldn’t drain the battery under normal circumstances, but in an already marginal situation, it can definitely make a difference.