You need to run a car to charge the battery. If you jump it, then only do a short journey, you won't have charged the battery. Then if its very cold, it will drain the battery, and old battery quicker than a new one.
Last time, my battery actually froze. When it thawed out the next day it started fine. This cold spell it wouldn't start again. Its a fairly new battery so I was puzzled. Turned out not to be the battery, but the connection to the battery was cracked and not making a good contact. Fixed that and its fine again.
An auto electrician will tell you if the battery is holding its charge, and if the car is charging it properly. They'll know in a couple of minutes.