Bukhari

Hadith Commentary:
Both nahr (slaughtering by stabbing in the throat) and dhabihah (slaughtering by cutting the throat) of a horse are permissible, and its meat is lawful (halal). However, since there is greater need for it in jihad, it is not customary to eat it generally.

Hadith Commentary:
(1)
The ruling for slaughtering a horse is the same as that for a cow, meaning that both nahr (slaughtering by piercing the throat at the base of the neck) and dhabḥ (slaughtering by cutting the throat) are permissible for it, but it is better to perform dhabḥ (slaughtering by cutting the throat).
(2)
From these hadiths, it is also understood that the terms nahr and dhabḥ can be applied interchangeably; thus, in the first and third narrations, the word nahr is used for the horse, and in the second narration, the word dhabḥ is used.
In any case, the horse is a lawful (halal) animal; both nahr and dhabḥ are permissible for it.
Since it is needed in jihad, it is not commonly consumed as food.
And Allah knows best.
(3)
Imam Bukhari rahimahullah, in the chapter heading, has referenced a narration from Ibn Abbas radi Allahu anhu stating that slaughtering is done at the throat and the windpipe.
Imam Bukhari rahimahullah has also indicated the weakness of a hadith in this regard, in which it is stated:
“If you strike it with an arrow or the like in its thigh, that is sufficient.”
(Sunan Ibn Majah, al-Dhaba’ih, Hadith: 3184)