I think you were slightly confused in your original question, that referred to "Winter Dreams" by Fitzgerald. There is no character called Emily in that story and so I think you were asking about "A Rose for Emily" by William Faulkner. I have edited the question accordingly.
In this story it is important to realise that Faulkner is very precise about when precisely Miss Emily's hair starts to turn grey. It is after Homer Barron has apparently deserted Miss Emily that her hair begins to turn grey:
When we next saw Miss Emily, she had grown fat and her hair was turning grey. During the next few years it grew greyer and greyer until it attained an even pepper-and-salt iron-grey, when it ceased turning. Up to the day of her death at seventy four it was still that vigorous iron-grey, like the hair of an active man.
The time referred to is crucial to the understanding of the readers of the last line of the story - we see how she has killed Home Barron and been "united" with him in death every night since his disappearance. Her greying also parallels her withdraw from the society of the living and her fading into the past or death. It could be argued that the reference made to the "iron-grey" colour also reflects her iron will and her act of murder.