All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If the situation is as you mentioned in the question that these horses are for acquisition and not for sale, then there is no Zakah on them according to the correct opinion of the jurists because the Prophet said: “A Muslim is not obliged to give charity [here it means Zakah] on his slave or horse.” [Al-Bukhari and Muslim]
However, the majority of the jurists are of the view that there is no Zakah on the horses which are not prepared for trade even if they are grazing and kept for breeding, and whether or not they are used for carrying.
Allaah Knows best.