Dismay, appall, horrify, daunt mean to unnerve and check or deter by arousing fear, apprehension, or aversion.
Dismay suggests a loss of power to proceed either because a prospect is terrifying or disheartening, or, more often, because one is balked and perplexed or at a loss concerning how to deal with a situation.
Appall, in its most forceful use, implies an overwhelming and paralyzing dread or terror. The word more often implies the sense of impotence aroused when one is confronted by something that perturbs, confounds, or shocks, yet is beyond one’s power to alter.
Horrify may emphasize a reaction of horror or of shuddering revulsion from what is ghastly or hideously offensive.
Often horrify comes close to shock in meaning and implies momentary agitation occasioned by a surprising breach of the proprieties or decencies.
Daunt presupposes an attempt to do something that requires courage and implies therefore a checking or scaring off by someone or something that cows or subdues.
Daunt perhaps most often occurs in negative constructions.