I already covered the barbecue so I won't beat that bush. But again for humidity control you don't want mass inflow of air. It brings more moisture in and in a heating climate ruins your efficiency. Since its for a heated area a dehumidifier would work well. As a plus the dehumidifier will produce some heat. In a cooling enviroment you don't want a dehumidifier as it basically is an ac the doesn't actually cool and adds heat. An actual ac is better (and not much more power consumption) in a cooling environment if it's not oversized.
The best of both worlds is a heat pump mini split. Models such as the hyper heat from Mitsubishi have heat down to -13f, have a dry mode that dehumidifies, and ac, all more efficiently than you resistance heater.