Hochreither attended the natural science department of the Staatliches Gymmasium Speyer (altsprachlich und naturwissenschaftlich), the present Gymnasium am Kaiserdom [de].
After his Abitur in 1952 he studied German language and literature, history and philosophy at the Albert-Ludwigs-Universität Freiburg and afterwards church music at the Hochschule für Musik Detmold, where he became a student of Michael Schneider, with whom he had a lifelong friendship.
Originally intended as Graf's successor, he moved to the Spandauer Kirchenmusikschule in 1963 as a lecturer for artistic organ playing and taught there until his retirement in 1998.
From 1964 to 2001, he was the successor of Hanns-Martin Schneidt and Helmuth Rilling and directed the [Bach-Chor_an_der_Kaiser-Wilhelm-Gedaechtniskirche] in Berlin and the Kirchenmusik at the Hochschule für Musik Detmold.
As Artist in Residence he was a guest of the University of Western Ontario in Canada and the "Asian Institute for Liturgy and Music" in Manila.