Extreme cold by itself will not cause battery failure. If the battery is discharged for any reason, such as the alternator did not fully charge the battery last time the engine was run, perhaps something was left ON last time the engine was running or possibly even the battery had an internal short, then another condition can enter into the situation. A battery cell can freeze and crack the case if the cell is allowed to completely discharge. Also, if the cell completely discharges then sits for a period of time, the plates in the cell can "sulphate", making them unable to ever take a charge again. Understand that a battery is nothing more than a storage device. It does not MAKE electricity, it only stores what was produced by the alternator.
the alternator is out
You left the light or something on last night and ran out the battery or your battery died
Discharged battery possibly or trouble with starter.
Alternator is no longer working properly.
No
Bad Battery. Bad Alternator. Lights left on by mistake. Something left running. Exc.
A dead cell in the battery will cause this. Also, any light that is on pulling power from the battery. Another possibility is a stuck relay.
AC runs on the battery. If the car is off and you run the AC, then start the car, it will stall.
Headlights run off the battery not the ignition...
battery
If the alternator fails, it is no longer keeping the battery charged and your engine is running on nothing but battery power. Once the battery runs down, your engine will no longer run.
I would say yes