Regards to batteries...

My first boat with shore power. I intend to use a 30-15 AMP converter and just plug the boat in over the winter. I'm assuming the onboard battery charging system is all automatic and won't have to do anything. Plug it in, turn on the main 30 AMP switch in the cabin and call it a day?

Not sure if a constant charge for months at a time is a good idea. I would feel better with a 30 minute trickle charge once a week.

I've always used an automatic battery tender and an extension cord all winter. I guess that's what I'm asking.....is the shore power constantly charging or only when needed?

That depends on the battery charger, but more than likely it has a 'float' stage.

I would leave mine plugged in to shore power with the battery charger off but a small de-humidifier plugged in and running. About once a month I'd go in and turn on the charger but leave one interior light on while the charger was on......but I'd also replace the batteries every 2-3 years regardless of condition or if any problems had occurred.

You should be fine just leaving it plugged in to shore power. The charging system should only charge when there is a draw on the system. Or at least the system on the 53 carver I work on, only charges the batteries when something is drawing on them. Otherwise it just maintains if they start to deplete.