Praise be to Allah.
The udhiyah is prescribed for both men and women. If a woman can afford to offer the udhiyah it is prescribed for her to do so, and if a woman offers the udhiyah, she should do it on her own behalf and on behalf of the members of her household, which includes her husband.
Shaykh Ibn Baaz (may Allah have mercy on him) was asked: Is the udhiyah for the family as a whole or is it for each adult family member? And when should it be slaughtered? Is it stipulated that the one who is going to offer it should not remove anything from his nails or hair before slaughtering it? If it is being offered by a woman and she is menstruating, what should she do? What is the difference between udhiyah and charity in this regard?
Offering the udhiyah is a confirmed Sunnah which is prescribed for men and women alike. One udhiyah is acceptable on behalf of a man and the members of his household, and on behalf of a woman and the members of her household, because the Prophet (blessings and peace of Allah be upon him) used to offer udhiyah every year, sacrificing two horned rams that were white speckled with black, one on behalf of himself and the members of his household, and the second on behalf of all those who affirmed the Oneness of Allah among his ummah. The time for offering the udhiyah is the Day of Sacrifice and the days of at-Tashreeq every year. The Sunnah for the one who offers an udhiyah is to eat some of it, give some of it as a gift to his relatives and neighbours, and to give some of it in charity. It is not permissible for the one who wants to offer an udhiyah to remove anything from his hair, nails or skin after the beginning of the month of Dhu’l-Hijjah until he offers his udhiyah, because the Prophet (blessings and peace of Allah be upon him) said: “When the month of Dhu’l-Hijjah has begun, if one of you wants to offer an udhiyah, let him not remove anything from his hair, nails or skin until he has offered his udhiyah.” Narrated by Imam Muslim in his Saheeh, from Umm Salamah (may Allah be pleased with her). With regard to someone who has been delegated to offer the udhiyah, or someone who is in a waqf (charitable organisation established to offer the udhiyah on behalf of anyone who wants to offer udhiyah), such a person does not have to refrain from removing anything from his hair, nails or skin, because he is not the one who is offering the udhiyah; Rather this is required of the one who is offering the udhiyah and appointed him to slaughter the animal on his behalf. The same applies for one who works for a charitable organisation that offers the udhiyah on behalf of others. He is a deputy acting on behalf of someone else, and is not the one who is offering the udhiyah. And Allah is the Source of strength.
End quote from Majmoo‘ al-Fataawa by Ibn Baaz (18/38)
But if you want to offer the udhiyah on his behalf, in the sense that the udhiyah is done for him, then it is essential to have his permission, because it is not permissible to do an act of worship on behalf of someone else except with his permission, regardless of whether the one who is doing it on his behalf is a man or a woman, because the udhiyah is an act of worship, and in all acts of worship there must be an intention.
And Allah knows best.