The use of horror in both of these stories seems to be rather different. In "The Rocking-Horse Winner," the horror is based on the supernatural nature of the rocking-horse and how the mother's lack of love leads the boy to desperately try and gain more money for her. In "Where Are You Going, Where Have You Been?" the horror is reflected through the complete domination of Arnold over Connie and how he comes to command her in every sense.
In "The Rocking-Horse Winner," the use of supernatural is used to create an atmosphere of horror, as we see Paul driven to ever greater excesses to try and find out the winning horse. The more he rides on his special rocking-horse, the more he is presented as being possessed and the more he sacrifices of himself. Note how his final fateful horse ride is described as his mother enters:
Then suddenly she switched on the light, and saw her son, in his green pajamas, madly surging on the rocking horse. The blaze of light suddenly lit him up, as he urged the wooden horse...
He cried out in a "powerful, strange" voice and his eyes "blaze" before he falls of the horse, unconscious. This element of the supernatural and the way in which riding the horse in this tormented way somehow communicates the name of winning horses to him add a real sense of horror as we see a boy sacrifice himself to try and gain his mother's love and affection.
The horror in "Where Are You Going, Where Have You Been?" does not have any reference in the supernatural. Rather, it is based around the complete dominance of Arnold over Connie as he manipulates her and makes her yield to him. The way that Connie is so unsure about her identity makes her ripe for the picking from Arnold's perspective, and perfect for his violent intentions. Arnold's words form an "incantation" that completely takes Connie in as she is hypnotised by his words, threats and blandishments:
The place where you came from ain't there anymore, and where you had in mind to go is cancelled out. This place you are now--inside your daddy's house--is nothing but a cardboard box I can knock down anytime. You know that and you always did know it. You hear me?
The true horror of this excellent story lies in the way that Arnold is able to prey on the weakness and unsure nature of Connie's character, resulting in Connie's complete yielding herself up to Arnold and her incredibly uncertain future, as the story ends with her realisation that she will see "so much land."