The author, D.H. Lawrence, uses an unnamed, third-person omniscient narrator. He makes an interesting shift, however, after the opening paragraphs, allowing a sense of his own point-of-view to permeate the narration with the introduction of Paul, the central character, while still technically maintaining the position of the third-person omniscient story-teller.
The story begins like a fairy-tale-like tone, with the introduction of "a woman who was beautiful, who started with all the advantages, yet...had no luck". The characters and the situation are introduced in a detached manner, simply and straightforwardly; a tale is about to be told.
After the fourth paragraph, the narrator's tone takes on a slightly sinister aspect, with the insistent repetition of the unspoken phrase which haunts the house - "There must be more money! There must be more money!" The whispered mantra is heard everywhere, and by everybody, even the most innocent, - the "big doll...in her new pram", and "the foolish puppy...that took the place of the teddy bear".
With the introduction of Paul in the eighth paragraph, the author incorporates dialogue in the narrator's presentation of interaction between characters. At this point, although the narration remains in the third person, there is a more personal, involved tone to the story, with the author allowing his own message to be expressed.
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The mother's voice informs the narration. Her resignation, her disappointment, her resentment, her excuse-making--even her third person stance underscores the distance she feels from the family. Also, she's the only character not named, sort of like like the camerman's not in the picture he takes. So the story that seems to be about Paul is really about the mother and about how Paul's death is not her fault and how he's probably better off dead anyway. She couches her thoughts in her brother's words for plausible deniability, but all in all, she sees the winnings she has as a result of Paul's naming the horse as "the good."
So the rocking-horse winner turns out to be not Paul but the mother, who's thinking she's finally got it not too bad, if she does say so herself.