Q) If my nails are cleaned thoroughly before I go to mikva do I also need to cut them?
A) The Shulchan Aruch (YD 198:20) tells us that a fingernail itself [when clean] is no issue of chatzitzo for tevila – even if the nail is large and protrudes over the end of the finger, and even if one intends to cut the nail at a later stage.
The Remo (ibid) emphasizes that this is only in a situation where there is no dirt at all under the nail.
The Taz (s.k. 20) explains that the reason a nail is not chotzetz even when it is large and protrudes is because it is a natural part of the body and similar to hair that is not intrinsically chotzetz.
[The above applies to a nail that is still completely attached to the finger (or toe). If the nail has slightly separated from the finder, and most of it is still attached – the Shulchan Aruch rules in the next se’if that the nail itself is chotzetz.]
The Remo rules that since the established minhag is to cut nails before tevilah, even if one forgot to cut a single nail and was tovel without cutting the nail – she needs to repeat the tevila.
According to the Taz, if a lady intends to be tovel on Friday night, and she forgot to cut her nails before Shabbos, she may not ask a non-Jew to cut her nails for her on Friday night. Instead, she should clean underneath her nails thoroughly and be tovel without cutting her nails. The Taz clearly learns that nails intrinsically are not a chatzitzoh and therefore if she is not able to cut her nails she can be tovel without cutting her nails – as long as they are clean.
The Shach (s.k. 25) however maintains that even in an ex post facto situation where she has already been tovel – she should still cut her nails and be tovel again. Only in a situation where it is not possible for her to be tovel again do we allow (b’dieved) a tevila with untrimmed nails.