OBK,
Never had this happen on an aircraft, but seen similar on cars several times.
Could you describe the symptoms a bit further? You said you were turning the engine over, but "nothing, not even a spit". Does this mean the engine was turning? Because if it was, it isn't a flat battery. As 2D says, the mixture-off procedure is for a flooded engine, and probably means you've over-primed the engine, or possibly left the throttle too high.
If your battery is genuinely going flat in the cold weather, you'll need a new battery. But I think, if you are actually having battery problems, it's more likely to be caused by the fact that you're turning the engine over for a lot longer than usual, because your priming procedure isn't getting the engine started.
FFF
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