While Franz Schubert (1797 - 1828) is an early Romantic, he is also a member of the First Viennese School.
Schubert idolized the works of Haydn, Mozart, and Beethoven and was a devotee to the latter – even serving as a pallbearer at Beethoven's funeral.
He was monumental in the development of Romantic forms, especially the song cycle. Despite being popular today, he gave only one concert of his own works before his death at age 31. He died completely unknown outside of Viennese society.
Schubert's inclusion in the First Viennese School is a touch controversial because his style – while rooted in the pillars of Viennese Classicism – is largely Romantic. Schubert had his own emotional world and artistic voice, but he died young – the year after Beethoven – a fact that seems to cast him in the latter's shadow.
Austrian musicologists consider Schubert part of the First Viennese School; however, having grown up outside of Austria, I have struggled with thinking about Schubert in the same breath as Haydn, Mozart, and Beethoven. But, his aesthetic and spirit are undeniably Viennese.