Q) Can I cut nails on chol hamo’ed?
A) The Shulchan Aruch (OC 532:1) permits cutting nails on chol hamo’ed in the normal fashion (i.e. without requiring a shinui).
The Remo (ibid) says that the prevalent minhag is to forbid cutting nails on chol hamo’ed. The exception to this is cutting nails in preparation for tevilas mitzvah – where nails can be cut even on chol hamo’ed.
The Mishna Berura (s.k. 2) explains that the reason of those who prohibit cutting nails on chol hamo’ed [i.e. the Remo] is so that one should not look unkempt on Yom Tov. This means that just as we find a rabbinic enactment that prohibits cutting hair on chol hamo’ed in order to ensure that one should not plan to cut one’s hair on chol hamo’ed – and this will cause him to begin Yom Tov without having a haircut; so too the same concern applies regarding nails: Were one to be allowed to cut nails on chol hamo’ed there is cause for concern that one may postpone cutting one’s nails until chol hamo’ed and will therefore begin Yom Tov unkempt (as a result of overgrown nails). In order to prevent this from happening Chazal prohibited cutting hair and nails on chol hamo’ed in order that everyone should cut their hair and nails before Yom Tov, and thereby begin Yom Tov looking presentable.
The Mishna Berura adds an important concession: that one who cut their nails before Yom Tov is allowed to cut them again on chol hamo’ed.
Another point that should be noted is that the prohibition of cutting nails on chol hamo’ed applies specifically to cutting nails with scissors or nail clippers. If one wishes to cut their nails on chol hamo’ed with their teeth, or to trim the nails by pulling them off – they may do so (Mishna Berura s.k. 3).