Does one need panim chadoshos at a Sheva Berachos on Yom-Tov and Chol Hamoed?
The Shulchan Aruch (Even Ha-Ezer 62:8) rules that on the first (and second outside Eretz Yisrael) day of Yom Tov there is no need for panim chadashos, because the day itself is considered panim chadashos.
This ruling follows the rationale of Tosafos, whereby Shabbos is considered panim chadashos because of the special joy and festivity of the day. According to the Ran, Shabbos is considered panim chadashos because Hashem called it panim chadashos, and based on this, Yom Tov will not be considered panim chadashos. An opinion that rules accordingly is cited in the Beis Yosef, but, as mentioned, the Shulchan Aruch rules that Yom Tov is considered panim chadashos (see also glosses of the Vilna Gaon to the Shulchan Arcuh, loc. cit.)
The question of Chol Hamo’ed is discussed at some length in Shut Betzel Ha-Chochmah (2:1). His ruling is that concerning Chol Hamo’ed of Pesach there is no question that the days are not considered panim chadashos, because there is no new joy for each day. Concerning Chol Hamo’ed of Sukkos, however, he writes that the days are possibly considered panim chadashos, on account of the special joy of each day.
Because the matter is unresolved, one cannot rely on the days of Chol Hamo’ed being panim chadashos, and the sheva berachos are only recited if an actual panim chadashos is present.