This certainly does seem to reflect a common pattern where fairy tales are concerned. You can also seen a similar element in other tales, such as the tales of Cinderella (with the stepmother) and Hansel and Gretel (with the witch).

With the story of Snow White, I think this theme is quite clearly expressed. After Snow White's mother dies, her father takes a second wife. When Snow White is seven, the Queen instructs a huntsman to kill her stepdaughter and bring back Snow White's heart. Later, when she discovers that Snow White has survived, the Queen disguises herself as an old woman, making several attempts to murder Snow White herself. One can see this theme quite clearly in this story, with the Queen's malice against Snow White and her repeated attempts at murder.

With the story of Sleeping Beauty, this question becomes more complicated (especially depending on which version of the story you're reading). In the tale of Briar Rose, the famous Grimm rendition of the story, I actually think this analysis breaks down. As the story goes, after Briar Rose is born, her parents invite twelve of the thirteen "Wise Women" (this is the wording given by Margaret Hunt; I've also seen them referred to as fairies). The thirteenth, slighted, arrives to place a curse on young Briar Rose. Here, however, even while the last of the Wise Women is malicious, the other twelve are portrayed as benevolent towards Briar Rose. Indeed, note that originally, Briar Rose's curse had actually been a death curse. It was only by the intervention of the twelfth of these women that Briar Rose could survive at all. Unable to counter the curse entirely, she instead transforms it into one of enchanted sleep.

That being said, the analysis probably fits better with the Perrault version of the tale, which makes specific reference to the evil fairy's advanced age. In addition, however, the Perrault version also includes a second, less-well-known half, in which after the princess has awakened and married, she becomes terrorized by her husband's mother, who is in fact depicted as an Ogre, intending to murder and eat her daughter-in-law and grandchildren. This Perrault version, with the elder fairy and the evil mother-in-law, far more strongly reflects the pattern of old women being evil than that of the Grimms.