Kulthum bin al-Aqmar (may Allah have mercy on him) says: The first person to distinguish the Arab horses (in the shares) was a man from among us called Mundhir al-Wadi'i. He was the governor of Sayyiduna Umar (may Allah be pleased with him) over some areas of Syria. He pursued the enemy; the (Arab) horses caught up, and the non-Arab horses fell behind. So he allotted a share for the (Arab) horses and left out the non-Arab horses, and wrote to Sayyiduna Umar (may Allah be pleased with him), who replied: What you decided is excellent. So it became the practice. Imam al-Shafi'i (may Allah have mercy on him) says: Our view on this is that Arab and non-Arab horses, and the horse whose dam is Arab and sire non-Arab or the reverse, are all to be treated equally; and if we were to accept such a report as established, we would not oppose it.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب السير / 17960
It is narrated from Sayyiduna Habib bin Maslamah (may Allah be pleased with him) that the Prophet (peace and blessings be upon him) "classed the Arab horse as Arab and the hybrid as hybrid."
Ahmad bin Abi Ahmad al-Jurjani, a resident of Hims, narrated it in this way from Hammad bin Khalid with a connected chain, whereas al-Shafi'i, Ahmad bin Hanbal and a group narrated it from Hammad with a broken (munqati') chain.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب السير / 17961
Sayyiduna Aishah (may Allah be pleased with her) says that the Messenger of Allah (peace and blessings be upon him) gave nothing to the kawdan (hybrid horse), and gave the Arab horses (their share) without it. The kawdan is "al-birdhawn al-bati'" (the slow non-Arab horse).
Abu Bilal al-Ash'ari is not used as evidence.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب السير / 17962
Sayyiduna Urwah bin Abi al-Ja'd (may Allah be pleased with him) says that the Messenger of Allah (peace and blessings be upon him) said: "Goodness has been tied to the forelocks of horses until the Day of Resurrection, and the spoils too have been placed in their forelocks." This indicates that the spoils have been linked to the genus of horses, so hybrid horses too are in origin of the horse breed.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب السير / 17963