Yes cold weather can cause a drain on a car battery and the colder the weather gets the more drain on your cars battery.
Your battery works through chemical reaction and during cold weather the chemical reaction in your cars battery slows down.
That makes the battery drain down to where it's either almost dead or even completely dead.
When the weather is cold you should keep a trickle charger on the cars battery if possible so that the battery doesn't drain down.
If your battery is 5 years old or older then replacing the battery would also be a good idea because batteries do eventually go bad and need replaced.
When the weather temperature gets to 32 F your cars battery loses at least 35 percent of it's strength and when the weather gets to 0 F your cars battery can lose as much as 60 to 65 percent of it's strength.
I always have trouble with my cars battery going down when it's cold outside and if the battery is 5 years old then I replace it just to prevent a totally dead battery.