Most AAA (American Automobile Association and its Afilliates)trucks carry a battery load tester, and the driver can quickly determine if the battery is toast or if they can give the customer a boost and then tell him to drive the car for 10 miles or so to charge the battery.
In cold weather the battery appears to run down quicker, but that's reallly the need for more juice to start the car. Just talked to my son who is at a cold ski resort in the Rocky Mountains. His 2004 Mazda 3 has 95,000 miles on it and is sluggish in starting. He had not noticed this at home where the car sits in the garage with a much higher temperature. He likely needs a new battery.
In other words, a simple load test will determine if ypour battery is on its way out. Checking all connections, which my AAA driver did as well, can determine if there ia a problem somewhere else. He even carries a sturdy rod to poke the starter if it has a sluggish solenoid.