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