Old fashioned converters which put out a constant voltage tend to boil off battery water and if you don't refill them regularly they will destroy your battery. If you have one of these types of converters then unplugging is probably wise or make sure you monitor water levels frequently. Newer multi stage converters don't deplete water (at least not very much) and they are safe to leave plugged in.
If you decide not to keep the converter on you might consider disconnecting the negative battery cable - that will keep things like alarms etc from depleting the battery - a fully charged battery will do fine in cold weather.
