In writing "The Horse Dealer's Daughter," D. H. Lawrence was strongly influenced by the work of the Italian author Giovanni Verga. Verga was renowned for his ability to capture peasant life, including the Sicilian dialect, and Lawrence wanted to do the same for the common folk of the English East Midlands with whom he had been familiar all his life.
Lawrence believed that writing dialect-laden dialogue gave the story an added touch of authenticity and local specificity. He also believed that it allowed him to capture the inner workings of the unsophisticated mind. And most of the various characters in "The Horse Dealer's Daughter" are unsophisticated compared to the city-dwellers of their day. These are rural folk who have no airs, graces, or pretensions about them. Their simplicity and lack of polish is meant to stand as a stark contrast to the worldly sophistication of the educated, middle-class Dr. Fergusson.
The use of dialect serves as a social marker, a way of highlighting the already significant differences between the likes of the good doctor and the members of the Pervin clan. Without knowing anything about their background, we can tell something about their social class as soon as they open their mouths and start speaking in an East Midlands dialect.