No Zakah on Horses (Ahadith 1201 - 1202)

Volume 2, Book 24, Number 542:
Narrated Abu Huraira (radiallaahu `anhu):
Allah's Apostle (sallallaahu `alayhi wasallam) said, "There is no Zakat either on a horse or a slave belonging to a Muslim".
Volume 2, Book 24, Number 543:
Narrated Abu Huraira (radiallaahu `anhu):
The Prophet (sallallaahu `alayhi wasallamsaid,"There is no Zakat either on a slave or on a horse belonging to a Muslim".
The animals on which zakaah is due are the an’aam animals, which are: 
  • Camels
  • Cattle, including buffalo
  • Sheep, which includes goats 
This applies if their number reaches the nisaab and they are put out to pasture, i.e. they graze and feed from plants on the land, and their owner does not purchase feed for them.
Other kinds of animals are not subject to zakaah unless they are for dealing and trading, in which case zakaah must be paid as for trade goods, such as a person who deals in ostriches, ducks, chickens, horses and so on. 
If they are an’aam animals that are given feed, but their owner trades in them, then he should pay zakaah as for trade goods, so he should work out their value when one year has passed and pay one-quarter of one-tenth of their value as zakaah. 
It says in al-Mawsoo’ah al-Fiqhiyyah (23/250):
The fuqaha’ are unanimously agreed that camels, cattle and sheep are the kinds of animals on which zakaah must be paid, and they quoted many ahaadeeth as evidence for that. There is a difference of opinion with regard to horses. As for mules, donkeys and other kinds of animals, no zakaah is due on them unless they are for trade. End quote.
More on the subject here.
As for the slavery part, go through this post.

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