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If you examine your initial statement, you would see that the answer to your ending question does not matter.

If an extremely cold day is climate change, and an extremely hot day is climate change, what is the point of the ratio?

I did not say that all extremely cold (or hot, for that matter) days are climate change.

Climate change is both an increase in global temperature (increased average), and an increase in extreme conditions (increased variance)

The number of extremely cold days increases, but the number of extremely hot days increases more, and both are relevant.