Schroeder was born in Bernkastel and spent the greatest part of his life’s work in the Rheinland. His mother's family had common ancestry with Beethoven. He studied from 1926 to 1930 at the Hochschule für Musik Köln, where his most important teachers were Heinrich Lemacher and Walter Braunfels (composition), Hermann Abendroth (conducting), and Hans Bachem (organ).
His main sphere of activity as composer, conductor and organist were supplemental to his work as a professor of choral conducting, counterpoint, and composition. Upon graduation from the conservatory, he obtained a post teaching music theory at the Rheinische Musikschule in Cologne. Eight years later he became organist at the cathedral in Trier. He remained in this post until the end of the war, adding the position of director of the Trier School of Music in 1940. After the war he taught music theory at the Cologne Musikhochschule beginning in 1946, becoming a professor there in 1948 and deputy director in 1958. He was also a reader at Bonn University from 1946 until 1973, and a lecturer at the University of Cologne from 1956 until 1961. He also conducted various semiprofessional ensembles such as the Bach-Verein Köln and the Rheinischer Kammerchor.
His notable students include Karlheinz Stockhausen.
Schroeder died on 7 October 1984 in Bad Orb aged 80.
Schroeder wrote a collection of Choral Preludes, focusing on the different seasons of the Church year - it's one of my favorite collections. This is the second one in the collection, Es ist ein Ros' Entsprungen.