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That question is impossible to answer. Too many variables to factor in: temperature of water, length of bath, size of subject (weight, bf%, etc), level of submersion, % brown fat vs. white fat, temperature of surrounding environment/air. I'm sure there are plenty more.
To know how much you would lose per ice bath, experiment. control as many of the above variables as you can for consistency from bath to bath, and test how much you lose. The weight change from pre- to post-bath likely wouldn't be what you would want to track (and may be hard to exactly measure, due to hair etc. retaining some moisture), but instead if you took the bath last thing before bed, took a pre-bath weight, consumed nothing else before bed, then took a morning weight after a fixed length of sleep, you may have a measurable result.
Report back when you have some solid data!