Indeed, a transvestite is a male or a female that dresses up in clothing from the gender opposite to their biological gender. They also adopt the normative opposite gender’s mannerisms. The word’s etymology is very explicit. It includes the prefix <em>trans</em>, which means across, through, beyond, in Latin; then the root word <em>vestite</em>, which comes from Latin <em>vestitus</em>, which means clothed.
Viola is a transvestite in as much as she disguises herself as a man and speaks and acts like one, while she is actually a woman.
Since transvestites are men who dress up as women, I am going to assume that the use of cross-dressing <span>makes Twelfth Night one of Shakespeare's transvestite comedies, and there are many of those, actually.</span>
