Who entrusted his armor and horses Xanthus and Balius to his closest friend at Troy?

The individual who entrusted his armor and horses, Xanthus and Balius, to his closest friend at Troy is indeed Achilles. In Homer's "Iliad," Achilles is depicted as a great warrior whose might in battle is paralleled only by his profound bond with his companion, Patroclus.

When Achilles withdraws from the fighting due to a dispute with Agamemnon, he is deeply affected by the war's progress and the fate of his side. After Patroclus dons Achilles' armor to inspire the Achaeans, he is ultimately killed by Hector. Prior to this, Achilles entrusts his prized horses and armor to Patroclus, highlighting the trust and closeness between them. This act symbolizes not only Achilles’ reliance on Patroclus but also emphasizes the themes of friendship and honor in the epic.

The other figures listed—Aeneas, Hector, and Odysseus—have their own significant roles and relationships within the "Iliad," but it is Achilles who is notably known for this specific act of entrusting his armor and horses to a dear companion.