Try an ad in the local paper "House sitter. Available Dec 01 - Apr 15. References and security check available. Contact 603-555-1234 em:
reliable@anymail.com "
Security and background checks are available through your local police for a fee. The cheapest is a "Pistol Permit" but if you show that, your prospective clients may take it the wrong way.
Alternatively... If you know somebody with a larger camper you might be able to borrow it for the off-season. If your town permits this, you could rig power and temporary sanitation connections on your home patch. Your heat expense will be higher than usual but it would still be less than renting.
Pity I didnt see this last week, Craigslist had two 60' mobile homes in the free listing!
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Found these on Craigslist. Not mine. Don't know who owns them. Don't care... They're examples of what you might use for temporary quarters.
http://nh.craigslist.org/rvs/1295419037.html http://nh.craigslist.org/rvs/1294786711.html
Hope this helps. Good luck!