It depends on which original story of Ariel you are referring to. In some versions, she might be depicted as having a certain complexion, but it can vary.
The original story of Princess Ariel is from 'The Little Mermaid' by Hans Christian Andersen. In the original, Ariel gives up her voice to the sea witch in exchange for legs to be with the prince she loves on land. However, the prince marries another, and Ariel is in great pain. In the end, she is given a chance to earn a soul by doing good deeds instead of a happily - ever - after marriage as in the Disney version.
Well, in the original tale, Ariel was indeed red - headed. This was part of her distinct character design from the start. Her red hair was not only a physical feature but also contributed to her overall charm and uniqueness in the story. It set her apart from other characters and became an iconic part of her look that has been carried over in many adaptations, although sometimes with slight variations.