This poem is distinguised from the majority of Whitman's verse because the narrator of the poem is a character who is not explicitly referred to and is somebody who we need to look very carefully at the poem to find out anything about. However, we can perhaps assume that the persona is somebody who is looking at the sight of the cavalry regiment crossing the ford from a great height. The image that is described is very broad, as the line of cavalry is described as a massive snake:
A line in long array, where they wind betwixt green islands;
They take a serpentine course--their arms flash in the sun--Hark to the musical clank...
This helps us to imagine the speaker watching this sight from a concealed vantage point as he looks down at the snake-like line of cavalry. Another point of interest about the persona is the way that he uses imperatives to urge the reader to "Hark" and "Behold" the scene that he describes. This implies that the sight is important somehow, as he is commanding us to pay very close attention to what is being narrated. Perhaps the clue to this lies in the final two lines of the poem:
Scarlet, and blue, and snowy white,
The guidon flags flutter gaily in the wind.
The "guidon flags" were the flags held by regiments to distinguish them from the enemy in the heat of battle. Perhaps the description of the flags has been delayed until the end of the poem precisely because this is what the speaker has been waiting to see. Now that he can identify the colours, he now knows that the cavalry he sees are friends, as indicated by the flags fluttering "gaily in the wind," rather than enemies. The persona of this poem is therefore perhaps a soldier trying to distinguish whether the cavalry regiment he is looking at are friends or foes.