When Stephen thinks of "The oval equine faces, Temple, Buck Mulligan, Foxy Campbell, Lanternjaws," the references to people are clear enough but his purposes in mentioning them are obscure. Temple was one of the students at UCD (University College, Dublin) who companioned Stephen in Part V of A Portrait of the Artist as a Young Man. Buck Mulligan is his present companion. And Father Richard Campbell was one of his teachers at Belvedere College, whom he thinks of in Part IV of A Portrait as a jesuit "whom some of the boys called Lantern Jaws and others Foxy Campbell."
Mulligan's face was described in Telemachus as "equine in its length," and in A Portrait Temple has "dark oval eyes," so these two characters are responsible for Stephen's thought of "oval equine faces." Campbell is mentioned only briefly in A Portrait, as Stephen imagines becoming a jesuit priest himself and experiences the "mental sensation of an undefined face or colour of a face. The colour faded and became strong like a changing glow of pallid brick red. Was it the raw reddish glow he had so often seen on wintry mornings on the shaven gills of the priests? The face was eyeless and sour-favoured and devout, shot with pink tinges of suffocated anger." He thinks that he may have derived this apparition from the face of Father Campbell.
The amalgamation of these three faces into one raises more questions than can be easily answered. Is Stephen thinking of his near escape from the clutches of the priesthood? His reflection that Beauty does not reside in the theological tomes of Marsh's library, within "the cathedral close," is followed by nearly three paragraphs of thoughts about priests and his own "awfully holy" phase. And Mulligan was imitating a priest in Telemachus when Stephen thought of his face as "equine." But nothing beyond Temple's name connects him to the clergy. This "gipsy-like student" who hangs on Stephen's every utterance is a socialist and a Republican, and strongly anti-clerical.
According to Ellmann, Temple was modeled on a Dublin medical student named John Elwood who kept company with Joyce and Gogarty in 1903 and 1904, and other scholars (Kathleen Ferris, Gordon Bowker) have written about this man's minor role in Joyce's life and writing. So the conjunction "Temple, Buck Mulligan" makes sense. But a generalizing inference that the "oval equine faces" belong to young men who have briefly attached themselves to the artist's genius is negated by the presence of Father Campbell, and makes little sense in the context of Stephen's thoughts in this section of Proteus.
Still more questions attach to the equine imagery. Stephen imagines Jonathan Swift not merely as a Gulliverian horse-lover but as himself a horse, running from the irrational mob to "the wood of madness, his mane foaming in the moon." He associates the brilliant Swift with the brilliant Joachim, another member of the clergy: "Abbas father, furious dean, what offence laid fire to their brains?" It is not entirely clear what kind of balance Stephen is striking between admiration for the genius of these two writers and dismay at their (essentially religious?) flight from the all-too-human. Things become murkier still when he associates Swift, and by extension Joachim, with the "equine" Mulligan, Temple, and Campbell. Did any offense lay fire to the brains of these three?