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Sea ice formation is complicated for several reasons, but to answer your question (I think), there really isn't a change in density of the water below the ice.

When it initially forms, much of the salt in the sea water becomes frozen in the nascent sea ice (and can take years to drain out). The small change in salinity of the water right below the ice would balance itself by convection in the uppermost layer of the ocean. Obviously, if the sea ice is going to float then it's going to be less dense than any of the water beneath it.

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