Is one allowed to shave on Chol ha-Moed Pesah? What about clipping nails?
It is prohibited to take a haircut on Chol Hamo’ed (Shulchan Aruch 531:1-2), and according to many authorities, this includes shaving. However, Rav Moshe Feinstein (Iggros Moshe, Orach Chaim 1:163; based (among others) on Noda Biyhuda, Tinyana, 99-101) permitted shaving on Chol Hamo’ed for someone who shaved before Yom Tov, who shaves regulalry (every day or two), and who feels distress in being unable to shave during Chol Hamo’ed.
Concerning nails, Shulchan Aruch (532) rules that one may cut nails on Chol Hamo’ed, but Rema writes that our custom is to prohibit this, and this is therefore the custom of Ashkenazim. However, Be’er Heitev cites from Nachalas Shiva that one is regularly cuts nails on Erev Shabbos may do so on Chol Hamo’ed, and if there is a need (especially if nails were also cut before Yom Tov), one may be lenient (see Kaf Hachaim 5; Shemiras Shabbos Kehilchasa 66:33).