A characters costuming is an essential way of tapping into an audiences personal experiences. By giving a character a stereotypical costume, one that the audience already understands, then they can make the automatic assumption that the character is a part of the stereotyped group, and all that entails. Eg, A character in a police uniform carries with them connotations of authority, enforcing the law, justice/corruption, and is a beacon of hope and safety.
Horror often creates and uses very ordinary people, without anything that really makes them standout. This is a deliberate tool for two reasons. First, we are usually very ordinary people, so we identify with ordinary people on screen and thus care and identify with them. Secondly, we can take that a step further, and transpose ourselves into the character and live vicariously through their experiences. We know we are doing that when we start talking to the screen to try and 'save' the character - a common occurrence among teenage boys watching horror, because they want to show they are in control when they are feeling the tension and fear of the character.
Costume isn't limited to the clothes that a character wears, but also includes the objects that they use. The choice of objects that a character interacts with tells us something about them. A child with a doll is naive and young. A killer with a knife wishes to inflict pain. A demon who eats a baby is anathema to all that is decent.
Costume also includes the makeup and prosthetics (artificial body parts - horns, wings, fangs etc). These are used a lot in horror, primarily when constructing a 'monster' or adding supernatural elements to a character. These features are worth writing about when looking their use in creating fear in characters and/or the audience. Another use in horror is in showing injuries that a character sustains. A large part of horror is showing how fragile we are - we have all stubbed our tow, so understand a hole in the chest to be significantly more painful.
When characters have changes in their costume, we can see that they have changed as well. Standard changes in costume are usually in direct relation to the characters experience. An example would be a character who is being chased and having their friends die around them - here, we would see their clothes become increasingly dirty, bloody and torn, which serves to drive home the harrowing experience the character is going through. When a character completely changes outfit, this will reflect a change in the story, and reflect the characters attitude towards new settings, events and/or people.
A characters costume can also reflect the genre of the film. A sci-fi film would have spacesuits or technological gadgets, a fantasy film would have swords and armour etc. In horror, we have the 'everyman' character (as explained above), but the monsters presented have very unique or identifiable features. The literal monsters stand out because they directly tap into our fear of being eaten - you know the uniqueness of these monsters, as they often come to mond as soon as someone mentions the name of the film - think of Alien, Starship Troopers, Tremors, American Werewolf in London, Dracula etc. Equally as important to horror are the human monsters - think Freddy Kruger, Jason Vorhese, Leatherface, Michael Myers, Hannibal Lector etc - they all have distinctive costumes which are memorable and automatically trigger the memory of fear we had at the peak of their story.