Praise be to Allah.

It is not permissible for the one who wants to offer an udhiyah to remove anything from his hair, nails or skin, once the month of Dhu’l-Hijjah begins, until he has offered his udhiyah, because the Prophet (blessings and peace of Allah be upon him) said: “When the ten (days of Dhu’l-Hijjah) begin, and one of you wants to offer a sacrifice, let nothing touch his hair or skin.”

Narrated by Muslim (1977). 

With regard to combing the hair, if he combs it gently without deliberately causing hair to fall out, then that is permissible and there is nothing wrong with it, especially for women, because their need to wash and comb their hair is greater. 

But if dealing with the hair will cause hair to break or fall out, then it is not permissible, because that comes under the ruling on removing some of it, and the one who wants to offer an udhiyah is forbidden to remove anything of the hair; in that regard he is like the pilgrim in ihram. 

It says in al-Mawsoo‘ah al-Fiqhiyyah (11/179): If the pilgrim in ihram is certain that hair will fall out as a result of combing it, then there is no difference of opinion among the fuqaha’ that doing so is haraam in that case. End quote. 

Al-‘Iraqi said in Tarh at-Tathreeb (5/33): Undoing the hair and combing it are permissible when in ihram, if that will not lead to hair falling out. End quote. 

The scholars of the Standing Committee said: The one who wants to offer an udhiyah should not remove anything from his hair, nails or skin once the month of Dhu’l-Hijjah begins, until he has offered his sacrifice. As for combing the hair without cutting it, there is nothing wrong with that.

End quote from Fataawa al-Lajnah ad-Daa’imah (11/428) 

Shaykh Ibn Baaz (may Allah have mercy on him) was asked: I decided to offer an udhiyah but a few days after the beginning of Dhu’l-Hijjah I combed my beard and some hairs fell out when I combed it; should I comb it or not? 

He replied: If any hairs fall out of the beard when combing it, without you doing that deliberately, that is pardoned, because they are regarded as dead hairs. The same applies if any hair falls from the head or beard of the pilgrim in ihram when he does wudoo’ or ghusl, without him doing that deliberately; it is pardoned because it is dead hair. The same ruling applies to the one who decides to offer an udhiyah after the first ten days have begun. What is prohibited is deliberately cutting something of that after entering ihram or after the first ten days of Dhu’l-Hijjah have begun, for the one who intends to offer an udhiyah.

End quote from Fataawa Islamiyyah (2/713) 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked: What is the ruling on combing the hair during the month of Dhu’l-Hijjah, before offering the udhiyah, for one who is not doing Hajj? 

He replied: 

When the first ten days of Dhu’l-Hijjah begin, if a person intends to offer an udhiyah, then he is not allowed to remove anything of his hair, nails or skin. But if a woman needs to comb her hair during these days, and she intends to offer an udhiyah, there is nothing wrong with her combing her hair, but she should do so gently. Then if any hair falls out without intending it to, there is no sin on her, because she did not comb her hair for the purpose of making it fall out; rather it was for the purpose of making it neat, and the hair fell out without her intending it to.

End quote from Noor ‘ala ad-Darb (9/5 8) 

To sum up: 

Combing the hair is not haraam for the one who wants to offer an udhiyah. A woman should comb her hair gently, and if any dead hairs fall out, there is no blame on her. The same applies if any of her hairs break without intending them to; there is no blame on her. 

But if a person deliberately cuts the hair, or knows or thinks it most likely that combing will make some hair that is not dead fall out, then he should not do that. 

If the hairdryer helps with combing and tidying the hair, and will not cause any but dead hair to fall out, then there is nothing wrong with using it. 

But if it is known that using it will lead to breakage of the hair and causing it to fall out, then it is not permissible. 

See also the answer to question no. 83381. 

And Allah knows best.