There is a chance that you would be miserable in an average RV through a Maine Winter. Even with extraordinary insulating measures, a conventional RV furnace will be costly and inefficient. Trying to keep the plumbing operational with the existing infrastructure of the property would be a fool's errand.
I doubt you can accomplish it with $10K but I would build a garage/shop and outfit it with good insulation and in-floor radiant heat. The water for the heating system can be heated with a variety of fuel boilers or a good gas water heater. A Porta-Potty or composting toilet could take care of waste. It may also behoove you to have the structure plumbed. A regular toilet, shower, and sink could be added also. Your budget will dictate how many amenities are implemented but maybe some can be added along the course of your stint.
