When Can You Cut Nails in Dhul Hijjah?
Question

With regard to a Muslim who is not performing Hajj, what should he do during the first ten days of Dhu’l-Hijjah? Is cutting the nails and hair not permissible? Is putting on henna or wearing new clothes not permitted until after the sacrifice has been slaughtered?
Praise be to Allah.What should you avoid during the first ten days of Dhul Hijjah if you intent to sacrifice an animal? 
If the onset of Dhu’l-Hijjah has been proven and a person wants to offer a sacrifice, it is haram for him to remove anything from the hair on his body or to cut his nails or any part of his skin. It is not forbidden for him to wear new clothes or to put on henna or perfume, or to be intimate with his wife or have intercourse with her. 
This ruling applies only to the one who is going to offer the sacrifice, and not to the rest of his family, and not to the one whom he appoints to slaughter the sacrifice on his behalf. None of these things are forbidden for his wife or children, or for his deputy. 
No differentiation is made between men and women with regard to this ruling. If a woman wants to offer a sacrifice on her own behalf, whether she is married or not, then she should refrain from removing any hair from her body or cutting her nails, because of the general meaning of the texts which state that that is not allowed. 
This is not called ihram, because there is no ihram except during the rituals of Hajj and ‘Umrah, and the one who is in ihram wears the ihram garments and refrains from wearing perfume, having intercourse, and hunting, but all of these things are permissible for the one who wants to offer a sacrifice after the month of Dhu’l-Hijjah begins. He is not forbidden to do anything except cut his hair, trim his nails or remove anything from his skin. 
Umm Salamah (may Allah be pleased with her) narrated that the Prophet (peace and blessings of Allah be upon him) said: “When you see the new moon of Dhu’l-Hijjah , and one of you wants to offer a sacrifice, let him refrain from (removing anything) from his hair or nails.” (Narrated by Muslim, 1977) According to another version: “Let him not remove anything of his hair or skin.”  
The scholars of the Standing Committee said: 
“It is prescribed for the one who wants to offer a sacrifice , when the month of Dhu’l-Hijjah begins, that he should not remove anything from his hair, nails or skin until he has offered the sacrifice, because of the report narrated by the group apart from al-Bukhari (may Allah have mercy on them), from Umm Salamah (may Allah be pleased with her), that the Messenger of Allah (peace and blessings of Allah be upon him) said:  “When you see the new moon of Dhu’l-Hijjah, and one of you wants to offer a sacrifice, let him refrain from (removing anything) from his hair or nails.” According to a version narrated by Abu Dawud, Muslim and al-Nasai: “Whoever has a sacrifice to offer, when the new moon of Dhu’l-Hijjah begins, let him not remove anything from his hair or nails until he has offered the sacrifice” – whether he is going to slaughter the sacrifice himself or has asked someone else to slaughter it on his behalf. As for the one on whose behalf the sacrifice is being offered, that is not prescribed in his case, because there is no report to that effect. That is not called ihram, rather ihram refers to the one who enters ihram for Hajj or ‘Umrah or both.” (Fatawa al-Lajnah al-Daimah, 11/397, 398) 
The scholars of the Standing Committee were asked: 
In the hadith it says, “Whoever wants to offer a sacrifice or appoint someone else to slaughter the sacrifice for him, from the beginning of the month of Dhu’l-Hijjah, let him not remove anything from his hair, skin or nails, until he has offered the sacrifice.” Does this prohibition apply to all the members of a household, old and young, or does it apply to the adults only and not the children? 
They replied:
“We do not know of a version of the hadith which appears as mentioned in the question. The version which we know is narrated from the Prophet (peace and blessings of Allah be upon him), as reported by the group apart from al-Bukhari from Umm Salamah (may Allah be pleased with her), according to which the Messenger of Allah (peace and blessings of Allah be upon him) said: “When you see the new moon of Dhu’l-Hijjah, and one of you wants to offer a sacrifice, let him refrain from (removing anything) from his hair or nails.” According to a version narrated by Abu Dawud – which was also narrated by Muslim and al-Nasai – “Whoever has a sacrifice to offer, when the new moon of Dhu’l-Hijjah begins, let him not remove anything from his hair or nails until he has offered the sacrifice.” This hadith indicates that it is not allowed to remove anything from the hair or nails after the first ten days of Dhu’l-Hijjah begin, for the one who wants to offer a sacrifice. The first report includes a command to refrain, which basically implies that refraining is obligatory, and we do not know of any reason to interpret it otherwise. The second report includes the prohibition on removing anything, which basically implies that it is haram, and we do not know of any reason to interpret it otherwise. Thus it is clear that this hadith applies only to the one who wants to offer the sacrifice. As for the one on whose behalf the sacrifice is being offered, whether he is old or young he is not forbidden to remove anything from his hair, skin or nails, based on the basic principle, which is that these actions are permitted. We do not know of any evidence to the contrary.” (Fatawa al-Lajnah al-‘Daimah, 11/426, 427)
If you are not planning to offer udhiyah, do you have to avoid cutting nails?
None of these things are haram for the one who does not intend to offer a sacrifice because he is unable to. Whoever removes anything from his hair or nails although he plans to offer a sacrifice does not have to offer any fidyah (ransom), but he has to repent and seek forgiveness. 
Ibn Hazm (may Allah have mercy on him) said: 
“Whoever wants to offer a sacrifice , it is obligatory for him, once the month of Dhu’l-Hijjah begins, not to remove anything from his hair or nails until he has offered the sacrifice, whether that is by shaving, trimming or any other means. Whoever does not plan to offer a sacrifice is not obliged to adhere to that.” (Al-Muhallah, 6/3)
 Ibn Qudamah (may Allah have mercy on him) said: 
“Once this is established, then he should forgo cutting his hair or clipping his nails. If he does that, he should ask Allah for forgiveness, but he does not have to offer any fidyah, according to scholarly consensus, whether he did that deliberately or out of forgetfulness.” (Al-Mughni, 9/346)
Why should you avoid cutting nails in Dhul Hijjah?
Al-Shawkani said: 
“The reason behind this prohibition is so that all parts will remain to be ransomed from the Fire, or it was said that it is so that he will resemble the one who is in ihram. Both views were narrated by al-Nawawi, but he narrated from the companions of al-Shafi'i that the second view is a mistake, because (the person who wants to offer a sacrifice) does not keep away from women or stop putting on perfume or wearing regular clothes, and other things which the person in ihram refrains from.” (Nayl al-Awtar, 5/133)
And Allah knows best.