What is the perspective?

As he does with the speaker in several of his Civil War poems--"Bivouac on a Mountain Side," "An Army on the March," and "By the Bivouac's Fitful Flame"--Whitman employs the immediacy of a first-person speaker (or, in "Crossing," implied first-person), one who is both present within and apart from the actions of the army he is observing. Whitman is, in short, in the poem. In "Cavalry Crossing a Ford," the speaker observes the action of a cavalry unit from a distance, but close enough to catch the sounds and details of the movement:
They take a serpentine course, their/ arms flash in the sun--hark to the musical clank. . . .
The speaker's perspective--a middle distance--allows him to take in the totality of the scene and, at the same time, to focus on the sounds, sights, the postures, and even the sun-burned faces of the troopers as they cross the river. His perspective, then, moves him into the scene so that sensory details emerge--"the splashing horses loitering, stop to drink"--but he creates a word-picture of the cavalry unit's complete movement from the first troopers across to those waiting to cross who, as tired cavalry troopers do, "rest on the saddles."
And, also as is typical of Whitman, he places himself, or his speaker, solidly into the poem by commanding the reader to pay attention:
Behold the silvery river . . . Behold the brown-faced men. . . .
This is an implied first-person speaker who stands next to us and shouts that we need to be looking at particular images, as if we are standing beside him while he directs our attention to the details that will allow us to understand what sounds and sights accompany a cavalry unit crossing a ford. He is not writing a poem, and we are not reading it--he is, and we are, experiencing a moment in the life of a Civil War unit.
With this commanding tone and immediate perspective, he places us, as he has placed himself, in the world of this anonymous cavalry unit as it goes about the business of war. It is not reaching to argue that Whitman's skill as a poet derives, in part, from his ability not only to create masterful poems that touch our senses but also to take his readers into his poems--even if he has to nudge us to pay attention to certain sights and sounds.