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Can't you just put a thermostat down there (if there's not one there already), and set it low so the boiler will kick on once in a while? Shouldn't use that much fuel just to do that.
I don't think you want to turn the boiler off.
I cycle mine 2-4 times a day (with a programmable T-Stat), and it doesn't burn very much oil.
This will not only keep the zones from freezing, but the boiler will throw off enough heat to keep the basement above freezing (if insulated properly).
The hot water from the boiler circulating through the zones will also make sure that a zone won't freeze by keeping the water at least relatively warm when not circulating, whereas a circulator pump alone won't guarantee a zone won't freeze if cycled on and off a couple of times a day while being exposed sub zero temperatures.
One other thing to consider what if something happens and the stove shuts down/runs out of fuel/doesn't work during freezing weather?
At least even set to low the boiler would fire and save a freeze up, but if the boiler is off you have no backup.
Trust me you will lose more money in repairs after a freeze up than firing a boiler a couple of times a day, but this is just my opinion.