In the first episode in Ouran High School Host Club, Haruhi is introduced with very drab clothing and hair. She had explained in another episode of how, and I quote: "A brat put gum in my hair and it was just being a bother, so I cut it off." Thus, explaining why she has short hair. But this doesn't explain why she dresses badly. I understand how she needs to cross-dress to pay back her debt, but did she actually cross-dress to begin with?
With her clothes don't forget that Ouran High is a school for rich kids which one can assume their uniforms cost a bit aswell, probably tailor made for each individual from the finest material, something Haruhi just can't afford.
Having gotten gum in her hair just before school begins, she cuts it short and being unable to afford the expensive Ouran uniform, she wears shapeless, baggy clothing. With her messily-styled hairdo, large glasses (which once belonged to her grandfather) and masculine clothing, she's thought to be male and Haruhi does nothing to discredit this idea.
The glasses are because she does have bad eyesight and wears contacts throughout the series (as we see when Renge is making a film and Takami sees Haruhi shed a tear without needing eyedrops).
As for the reason why she "cross-dresses" before becoming a Host it's because she doesn't see it as cross-dressing because to her gender doesn't matter.
Two characteristics that define Haruhi is her straightforward nature and belief that one's gender doesn't define one's choices
This is also apparent when the Host Club go to the beach (a real one, not an Otori rehab clinic) and Haruhi stands up against a couple of guys who are harassing the girls. Haruhi doesn't see that her being a girl means anything different so with that mind set there is no male/female clothing, just clothing.
Of course one can also assume her transvestite father may have also left a bad impression of how girls/women really are.
From the wikia:
When first introduced in the anime, she sports a nerdy, boyish look that differs greatly from her middle-school appearance. Having gotten gum in her hair just before school begins, she cuts it short and being unable to afford the expensive Ouran uniform, she wears shapeless, baggy clothing. With her messily-styled hairdo, large glasses (which once belonged to her grandfather) and masculine clothing, she's thought to be male and Haruhi does nothing to discredit this idea.
Technically, Haruhi didn't cross dress. She wore "shapeless, baggy clothing", which were mistaken to be masculine because of her overall appearance. She does nothing to discredit this, thus being mistaken for a male.
The first part is how everyone mistakes her as a male at the start. However, Haruhi doesn't really think gender matters that much, thus has no qualms about her new uniform, or perpetuating this mistaken view.