Is It Permissible to Use Animal Horns?
Question

What is the ruling on horns that are cut from animals when they are alive or after they die, and using them for various purposes?
Praise be to Allah.Using horns taken from properly-slaughtered animals 
If the horns are taken from animals whose meat is permissible to eat, such as cows and sheep, after they have been slaughtered properly, then it is permissible to make use of them, and there is no difference of scholarly opinion concerning that.
Using horns from animals when they are alive 
But if the horns are cut from the animal when it is still alive, or are taken from it after it dies without being slaughtered in the prescribed manner, then there is a difference of scholarly opinion as to whether they are pure (tahir) or not.
The well-known view among the Malikis, Shafi'is and Hanbalis is that they are impure (najis).
It says in al-Mawsu‘ah al-Fiqhiyyah al-Kuwaitiyyah (39/391-392):
“The jurists differed concerning the ruling on making use of the bones, horns and hooves of animals whose meat is permissible, if those animals died without being slaughtered in the prescribed manner; there are two views:
The first view is that of the Shafi‘is, Malikis and Hanbalis, which says that they are impure (najis) and it is not permissible to make use of them.”
They quoted as evidence the fact that this is part of the animal that died without being slaughtered in the prescribed manner (maytah), so it is impure. The same applies if it is cut from the animal whilst it is alive; it comes under the ruling on maytah.
Ibn Qudamah (may Allah have mercy on him) said:
“Horns and hooves are like the bones: if they are taken from an animal that has been slaughtered in the prescribed manner, then they are pure, but if they are taken from a living animal, then they are impure, because the Prophet (blessings and peace of Allah be upon him) said: “That which is taken from an animal when it is alive comes under the same ruling as maytah (“dead meat”, i.e., from an animal that has not been slaughtered in the prescribed manner).” Narrated by at-Tirmidhi, who said: It is a hasan gharib hadith.” (Al-Mughni, 1/99)
The Hanafis and Imam Ahmad, according to one report narrated from him, are of the view that that is pure (tahir) and it is permissible to make use of it. Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) preferred this second view and said: This is the view of the majority of the early generations (the salaf).” ( Majmu‘ al-Fatawa, 21/96-102)
We quoted his words in abbreviated form in the answer to question no. 258312 .
Al-Bukhari (May Allah have mercy on him) said: 
“Az-Zuhri said: With regard to the bones of animals – such as elephants and the like – that die without being slaughtered in the prescribed manner, I met some of the earlier scholars who used combs made out of them and vessels for hair oil made of them,  and they did not see anything wrong with that.” (Fath al-Bari, 1/342)
Al-Hafiz Ibn Hajar (may Allah have mercy on him) said:
“The phrase “used vessels for hair oil made out of them” here indicates that they believed them to be pure (tahir).” (Fath al-Bari, 1/343)
Ibn al-Qayyim (may Allah have mercy on him) said:
“The reason why they were deemed to be pure (tahir) is that the reason why the maytah (animals that died without being slaughtered in the prescribed manner) is deemed to be impure (najis) is not applicable with regard to the bones, so they (the bones) are not deemed to be impure and it is not valid to compare them to the flesh, because the flesh is prone to decay and may exude foul matter, which is not applicable in the case of bones. This reasoning is more sound and stronger than the first, so based on that, it is permissible to sell the bones of an animal that died without being slaughtered in the prescribed manner, if they come from an animal that is pure in principle.” (Zad al-Ma'ad, 5/674)
The view that the bones and the horns of an animal that died without being slaughtered in the prescribed manner are pure (tahir) is a strong view, so whoever follows that view is not to be blamed, but if anyone decides to err on the side of caution and refrain from use of the bones or horns of an animal that died without being slaughtered in the prescribed manner, that is better for him, especially if he can do without them and can find an alternative to meet his needs.
For more on issues related to animals, please see these answers: 105419 , 111786 , 153936 , 95329 , 93387 , and 21417 .    
And Allah knows best.