Could you build a small 'room' in the basement with well-insulated floor, walls and ceiling? Stocked with cots, blankets, sleeping bags, etc? (and some food, water, lights, radio, batteries, past-times (books, playing cards, etc?). Your families body heat might keep it fairly warm. It could even be some type of 'safe' room, in case of a bad storm.
I have 2 kerosene heaters I bought at the end of the season from Home Depot. They cost me $77 each. They won't heat the whole house, but I figure they'll at least keep the pipes from bursting. I store my kero in my garage, with a stabilizer called Pri-D. So far, it's worked great.