One quick test to see if your converter is working is to turn on a light or two then if you have a battery disconnect switch, turn it off. If the lights stay on the converter is at least working. If no battery switch just disconnect the negative wire attached to the battery.
If the lights go out the converter is not operating. Check circuit breaker that feeds the converter.
FWIW, charging a battery is an electro-chemical reaction inside the battery. Cold can inhibit this process greatly. The electrolyte inside the battery needs to be 70-80 degrees before the battery really charges. Until them the energy you put into the battery is merely going into heating the battery.
Another factor is how temperature of the battery actually affects the Voltage the battery puts out at low temps. Unless your battery monitor actually compensates for battery temperature at 8 degrees your battery voltage may be low enough to fool the usual voltage only reading monitors. Here's a chart that shows the changes due to temp:
I'm assuming your batteries are standard Lead/Acid chemistry and are in an unheated area. If so this may be why you see the low state of charge.
Disconnecting the batteries and checking output of Converter would be my first stop. Should be over 13 volts. If so, your issue is most likely cold batteries. I the battery is outside some help may be possible if you have an old sleeping bag your can wrap around the battery box to help retain some of that heat the charger is trying to generate so the battery can accept a charge.
Good Luck
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