1. Put a battery charger on your battery; make sure it is topped off and is a good battery.
2. Check general condition of connections, particularly ground connections normally hidden such as those under the battery tray or other hidden spots. I can't direct you as I don't know your chassis generation at all.
3. Check the connections at the starter motor.
4. Do a double glow cycle if you can. If the battery can't handle that and still turn the engine over sufficiently quickly to start, then get a good battery with a sufficient amp-hour rating and try again. CA and CCA ratings don't tell the whole story - you need at least a good RC (reserve capacity) if you don't have an a-h rating.
5. To get the real story on error codes, get a VCDS for a scan that has lots better detail than generic OBD-II codes. But for electrical faults that sound strange like this, then getting your battery capacity back up to par is the best bet.
6. Check the alternator output. Best is to remove the alternator from the car and check its output directly, but since that is really difficult to do, the next best thing is to check the system voltage while the car is running. If you measure across the battery posts, it should read 14v while running. Best is about 14.2-14.4. Less than 14 gets marginal in a hurry in the winter because batteries need higher voltage to get a full charge when it gets really cold.
7. Consider changing the oil to a good 0w-30 qualified diesel oil (meets the specs you need). Others will argue a 0W-40 is the only weight you want, but 0W-30 will give you better initial performance (starter spins the engine faster) in the cold. If you do primarily long trips, maybe you would rather relax with 0W-40. OK, your choice. But a thinner oil will be easier to start the engine. Just sayin'. All of the other things above will probably be all you need to do.
Cheers and good luck,
PH