The story focuses on a complex relationship between Jenny and her uncle Ifor, where she comes to stay with him after her grandmother dies. The dresser mentioned in the title is a symbol of Ifor's Welsh heritage and his isolation.
The story does not involve a horse named Ashling, nor does it include a decision by Jenny to buy or not buy a horse.
Perhaps you are remembering a different story or have a misunderstanding about the events of "Uncle Ifor's Welsh Dresser"?