Shulchan Arukh Orach Chayim · Siman 531

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1. The Laws of Shaving on Chol Hamoed, 8 Seifim: It is a mitzvah to shave on the day before a holiday.

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2. One may not shave during the holiday, even if he shaved before the holiday.

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3. Even if one was forced and thus did not shave on the day before the holiday, he should not shave during hol hamoed. This is also the rule for one who was sick and got better during the holiday.

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4. The following people may shave during the holiday: he who left captivity and did not have an opportunity to shave before the holiday; he who left jail, even if he was imprisoned by Jews who would have allowed him to shave; he who was banned [formally by the community] and allowed [back into the community] during the holiday; he who vowed not to shave and asked for the nullification of his vow during the holiday; he who arrived from abroad during hol hamoed or who arrived on the day before the holiday but didn't have time that day to shave, assuming that he did not go from Israel to outside of Israel for recreational purposes.

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5. Even in instances where it is permitted to get a haircut, one should not get a haircut in the public domain. Rather, one should do this in private.

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6. A child can be shaved during the holiday, even if he was born before the holiday (and this is even allowed in public) (this follows from the Mordechai).

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7. If a mourner's seventh day [of mourning] falls on a Shabbat that is the day before a holiday, he is permitted to shave on hol hamoed. Rem"a: He who left Judaism, returned, and normally shaves is permitted to shave on hol hamoed (Trumat Hadeshen chapter 86).

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8. Every man is permitted to remove his mustache on hol hamoed. Rem"a: Even in public. It is permitted to rub the head and to comb even though this will remove hair - it is not considered shaving (Mordechai at the beginning of Moed Katan).