He said to her, "What a cold day!"

The given direct speech is: "What a cold day!"
To convert this into indirect speech, we need to consider the reporting verb, which is "He said to her."
In indirect speech, the reporting verb "said" changes to "told," and the exclamation changes to "exclaimed."
Also, the pronoun "her" changes to "her."
Now, we need to change the tense of the reported speech according to the rules of indirect speech. The exclamation "What a cold day!" does not have a direct equivalent in reported speech. So, we need to express the same idea using an exclamation or a suitable expression of emotion.
Among the options given, option D "He exclaimed that it was a very cold day." fits the best, as it uses the reporting verb "exclaimed" and adds the intensity of "very" to convey the idea of the speaker's surprise or emotion about the cold day.
Hence, the correct answer is Option D.