I recently made a mistake of starting my car, and only driving it for a short trip multiple times in below-freezing weather without letting the car fully warm up. This was after the car had sat for multiple weeks, so it drained the battery to the point where it could crank but not start in the cold. I made two attempts, but no dice. 2 weeks go by as I figure out what to do, then I used a battery jumper and it fired right up.
After that first start I took it for a good 30 min drive, after which it fired right back up, and has had no trouble since, but I'm afraid I may have done some damage by letting it get so low and not dealing with it for 2 weeks while it wasn't able to start.
The battery is at least 5 years old (that's when I purchased the car used), perhaps much older or even original (2010), but this was the first hiccup. Is it just time to replace it? Did I do some lasting damage, or am I overthinking it?