The following year, Goetz was appointed as city organist of Winterthur in Switzerland (thanks to the assistance of Carl Reinecke), where he taught the piano and began to make his name as a composer.

In 1868, he married, and two years later moved to the village of Hottingen, today a suburb of Zürich, but remained employed in Winterthur until 1872.

The conductor Felix Weingartner found it "incomprehensible that his delightful opera comique, Der Widerspänstigen Zähmung, should have entirely disappeared from the repertoire.

Although Goetz showed active interest in the important artistic trends of his own time (on the one hand Liszt and Wagner, on the other Brahms), his own compositional style was more influenced by Mozart and Mendelssohn, and to a lesser degree by Schumann.

Great mastery of compositional technique is characteristic of Goetz's style, which is particularly apparent in the connectedness of motifs and the technical depth of movements.