No, The Iliad does not directly narrate the Trojan horse.
It does not narrate the whole war either: it focuses on a crisis in the Greek camp.
The poem ends with Hector's funeral, before the fall of Troy.
The horse belongs to the Trojan cycle and the broader memory of Troy.
The Odyssey evokes it later, especially as one of Odysseus' deeds told after the fact.
What The Iliad really tells
The Iliad begins with anger, not with a landing. Achilles feels dishonored by Agamemnon, withdraws from battle, and his absence endangers the Greek army. The poem follows that wound through Patroclus, Hector and Priam.
Where the horse belongs
The horse belongs to the wider Trojan cycle: the group of stories that surrounded The Iliad and The Odyssey in antiquity. Part of that literature has vanished, but its matter survived through summaries, allusions, tragedy, images and Latin retellings.
In The Odyssey, the horse returns as remembered song. Among the Phaeacians, Demodocus sings the episode, and Odysseus weeps. The scene is brief, but it says much: the victor of Troy is not only proud of his trick; he is haunted by what it opened.
Why the confusion lasts
Because the horse has become the clearest image of Troy: a city taken not by strength, but by intelligence. And Odysseus is precisely the hero of that intelligence. Readers therefore tend to place all Troy under "The Iliad", when the tradition is wider, more fragmented and more interesting.
Place the horse within the Trojan affair
Questions around the horse
Does The Iliad tell the Trojan horse episode?
No. The Iliad ends before Troy falls; the horse belongs to the wider Trojan cycle and later traditions.
Why is Homer still associated with the horse?
Because The Odyssey evokes the horse as a reported story, and because ancient tradition connects Odysseus, Troy and the trick.
What does The Iliad actually tell?
It tells a late crisis of the war: Achilles' anger, Greek losses, Hector's death and Priam's final act.
Can Nolan's film show the Trojan horse?
Yes. Reported presentations have mentioned a horse sequence. That does not make the episode the narrative center of The Iliad.