I don't remember what I personally thought when I first read the passage (the ending of chapter II of Book III, 'The Riders of Rohan', for easier reference), but I daresay I believed the old man to be Gandalf due to Aragorn's words to Legolas, noting that the man had a hat and not a hood. Since Eomer had said that Saruman walked hooded, Aragorn's observation pointed in the direction of Gandalf.

But actually the old man IS Saruman, as confirmed by Christopher Tolkien in HoMe VII: The Treason of Isengard and by Hammond&Scull in their LotR: A Reader's Companion, which I will cite in full:

"Scheme [a manuscript time-scheme of the events in LotR made by Tolkien] confirms Gimli's suspicion: 'February 30: Saruman appears on battlefield and is seen by Aragorn and companions at night.' An earlier time-scheme, written while Tolkien was working on Chapters 7 and 8 of Book III, includes the entry: 'Aragorn and his companions spend night on the battle-field, and see "old man" (Saruman)' (The Treason of Isengard, p. 428). They are a considerable way from Orthanc and the reader might wonder with Gimli in Book III, Chapter 5 whether it was really Saruman or only 'an evil phantom' of him, especially as he leaves no traces. But Gandalf later explains that it was Saruman: 'He was so eager to lay his hands on his prey [the hobbits and possibly the Ring] that he could not wait at home, and he came forth to meet and to spy on his messengers. But he came too late for once, and the battle was over and beyond his help before he reached these parts. He did not remain here long' (Book III, Chapter 5)."

In HoMe VII Christopher Tolkien notes that in the earliest version of the text his father might have thought the old man to be Gandalf, because (among other reasons) in that version the horses were not lost and neither did they seem afraid.