Høgset holds degrees in language and musicology from the University of Oslo, 1974, as well as voice and choral conducting from the Norwegian Academy of Music, 1976. He was a student of the composer Knut Nystedt.
In 1971, Høgset founded the chamber choir Grex Vocalis, where he conducts to this day. In 2012 he was appointed, for the second time, conductor of the Norwegian Student Choral Society (first time 1982–1985). He has also previously conducted the Norwegian Youth Choir (1987–2003).
Høgset is himself a singer, with a career that stretches back to his youth, when he was a member of Sølvguttene. Høgset has, in later years, released a number of solo recordings of pieces by Henry Purcell, Georg Friedrich Händel, Edvard Grieg and Arne Nordheim.
As a lecturer, Høgset has taught both in state schools and the Norwegian Academy of Music and runs a number of courses and seminars for choir singers both in Norway and internationally.
- «Høgset utnevnt til Ridder», Ballade, 17. December 2007.
- «Awards for St. Olavs Order», kongehuset.no, 3 December 2007.
- The Norwegian Choir Society - 6 April 2014