Re: power inverter ?s
They do make 12 and 24VDC air conditioners. They are not cheap and they will require a large battery bank. Google "12vdc air conditioner". Big yachts that operate in the tropics actually have a heat exchanger connect to the hull.
Some people do run a small window A/C like you are referring, but only when they are anchored up in a calm area. They lash an inverter generator to the swim platform and shut id down once it gets dark.
The good news is that as hybrid vehicles become more common, 12VDC A/C is becoming more common in light vehicles. They are still very expensive compared to a traditional automotive A/C pump, but the price IS coming down. If you are a real DIYer, you might be able to get a compete system out of a salvage yard for under $500.