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Which ice Age? Do you mean the last glacial phase of the present one, ending about 10 000 years ago?
If so, the ice cover and Arctic fringe retreated, and the sea-level rose, to their present levels. Same processes as any of the Ice Age’s alternating freeze-thaw stages.
The extinctions of the large tundra animals like Mammoth were probably as much to do with Man hunting them as diminishing habitat and competition from other animals. The smaller animals were already around.