How bad are converters on batteries?

A modern multistage converter should be not hard on the battery at all for that length of time. It would be a good idea to check and top up if needed the battery electrolyte at the start if that hasn't been done recently.

Since this is winter in a relatively cold climate, you could also charge the battery fully and disconnect it for the few months of winter and it wouldn't self-discharge too much. But with power available it hardly makes sense to do that.