You'll need to don your detective hat for this one. Perhaps the first thing to do is to check the battery level to see if it is actually low or if the system is giving you a false reading. My guess is that some kind of system reset needed to be performed when you swapped the battery. Have a look at an owners' manual if you've got one.

If you find out the battery is low, then you need to look for something that could be causing it to drain - usual culprits are a boot light not going off properly (check by placing your phone in the boot and record a video to check it goes off) or look for an interior light that's staying on as well as any exterior lights not going out. Alarms and stereos can also drain the battery. What kind of driving are you doing? A battery needs 70-80% of its power to start a car on these cold winter mornings so if you're only driving a few miles (or under 30 minutes) then there's a good chance the system isn't able to recharge it. Try taking it out on a motorway. If all else fails, it could be a fault with the alternator - an auto electrician can help here.