Praise be to Allah.
If a person wants to offer an udhiyah, then it is haraam – according to the more correct view – for him to remove anything from his hair or nails until he offers his sacrifice, regardless of whether he offers his sacrifice at the beginning of the time for it, immediately after the Eid prayer, or at the end of the time, i.e., before sunset on the thirteenth of Dhu’l-Hijjah.
That is because of the report narrated by Muslim in his Saheeh (1977) from Umm Salamah (may Allah be pleased with her), who said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Whoever has an animal to sacrifice, when the new moon of Dhu’l-Hijjah appears, let him not remove anything from his hair or nails, until he has offered his sacrifice.”
Shaykh Ibn ‘Uthaymeen said: When the first ten days of Dhu’l-Hijjah begin, if you intend to offer an udhiyah on your own behalf or on behalf of someone else from your wealth, then you should not remove anything of your hair, either from the armpit or the pubic area or the moustache or the head, until you have offered your sacrifice. Similarly, you should not remove anything from your nails, either on the feet or on the hands, until you have offered your sacrifice. … That is a sign of respect for the udhiyah, and so that those who are not in ihram will attain some of what those who are in ihram for Hajj will attain, because when a person goes for Hajj or ‘umrah, he does not shave his head until the sacrificial animal reaches the place where it is to be slaughtered, and Allah, may he be glorified and exalted, wants to give His slaves who are not performing Hajj or ‘Umrah a share of the rituals. And Allah knows best.
Sharh Riyaadh as-Saaliheen (6/450)
And Allah knows best.