Free indirect discourse refers to a hybrid type of narration that resembles quoted speech, but technically resides in the realm of reported speech. In terms of point-of-view, it is third-person, meaning that it is told from the perspective of a narrator external to the events being reported. But the narrator gets so close to the minds of one or more of the characters that it almost seems like first-person perspective. Often, in free indirect discourse, the narration with flow in and out of different character's minds, and contain rhetorical questions or sentiments that sound like they are describing exactly what the character might be thinking in their head. Lawrence uses free indirect discourse in "The Horse-Dealer's Daughter" with Joe, Mabel, and Dr. Jack Ferguson.
In our own time, the literary world is even more concerned with the question of authenticity, especially when it comes to the perspectives of characters and narrators and how those perspectives align with the lived experience of their author. In the case of D.H. Lawrence, he was interested in the sensual and sexual—what the authorities at the time deemed to be obscene—private minds of his characters. Often, Lawrence wrote from or close to the perspective of female characters. So one question that people might ask now is, does Lawrence have the right to assume he knows what his female characters are thinking?
Many people feel that if writers are not allowed to write from the perspectives of people who are different from them, then there would be no fiction—or, at the very least, all fiction would be some exaggerated facsimile of the author's life. Other critics argue that if an author is going to venture outside of their own lived experience, then they must do so humbly, without making assumptions about different cultures and experiences. Novelist Hari Kunzru writes in The Guardian that, "Good writers transgress without transgressing, in part because they are humble about what they do not know. They treat their own experience of the world as provisional. They do not presume." So, the answer is more complicated than who can and cannot write from certain perspectives. The question becomes more about how the author treats their subject matter.
If we track the perspective of Lawrence's narrator in "The Horse-Dealer's Daughter," we may see that he began with the intention to criticize the typical masculine perspective that men should earn the money and women should occupy domestic roles and get married. It is clear that Lawrence isn't fond of the character Joe; Joe and the other siblings are portrayed as ignorant and dismissive of Mabel. However, the narration abandons Mabel's perspective a little more than halfway through the story, and from there on focuses on Dr. Ferguson's mind. In the end, Mabel is folded into the conventional goal of the time: finding a husband and achieving financial security. Mabel is sexualized by the end of the story, naked and crawling on the floor. So, regardless of Lawrence's intentions, we can ask whether he actually succeeded in making a feminist commentary, or if his story perpetuated sexist stereotypes.