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I wouldn't worry about the oils, they just slow it down, the worst that could happen with them is that they'd get thick enough to stop the watch. I'd be more worried about the freezing water (which expands) forcing its way into the case or damaging the case or seals. If nothing else, I certainly wouldn't want to do it over-and-over (as this would tend to wedge the case open, the same way that freezing water wedges rocks apart).
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