Why a horse? Because the patron god of Troy was Poseidon. Is everyone illiterate now?
Apollo was considered the god protector of Troy.
But why a horse? Because Troy was attacked by the Greeks and Poseidon was the Greek god of the sea, earthquakes, storms AND HORSES. So possibly, it was the Greek tales of Poseidon that provided Homer with the idea of Troy being attacked by a Greek horse.
In fact, there is a prominent Greek tale where Poseidon transforms into a horse to pursue the goddess Demeter.
Also, in fact, Poseidon is frequently credited with creating the first horse as a gift during his contest with Athena for control of Athens, which is why he is often called Poseidon Hippios (Lord of Horses).
Thus, Homer had in front of him tales of Poseidon masquerading as a horse in pursuit of a female (a goddess), and of Poseidon presenting a horse as a gift as part of trying to win control of Athens.
Possibly Homer - a Greek - then transmuted it all into a mythic tale of how Troy was defeated by the Greeks.
Homer was the “nationalistic” fake news Greek champion of his day, but he kept true to Greek mythology and thus was enjoyed and appreciated by the Greeks.