Heiða Árnadóttir has throughout her career placed strong emphasis on the performance of contemporary music, as well as folk, jazz, experimental, and art song. She completed her master’s degree at the Royal Conservatory in The Hague, the Netherlands, in 2004.

In addition to numerous concerts in Iceland — where she has premiered works with Ensemble Adapter and Caput, among others — Heiða has also performed in the Netherlands, Belgium, France, India, Sweden, and Denmark. She has appeared at the Nordic Music Days, Dark Music Days, Iceland Airwaves, Skálholt Summer Concerts, Reykjavík Opera Days, the Reykjavík Jazz Festival, and various international festivals, including a showcase concert at the WOMEX music festival in Copenhagen.

Heiða was nominated as Classical Singer of the Year at the Icelandic Music Awards for the years 2020 and 2023. She also received the Gríma Award for Singer of the Year in 2024 for her performance in the song cycle Mörsugur.

Heiða is a composer, lyricist, and vocalist in the band Mógil, which has released four albums. She was artist-in-residence at the Dark Music Days festival from 2020 to 2023, where she premiered numerous works by Icelandic composers.

In 2023, Heiða released the album Tunglið og ég (The Moon and I) in collaboration with pianist Gunnar Gunnarsson. On the album, they perform songs by composer Michel Legrand with Icelandic lyrics by Árni Ísaksson and Bragi Valdimar Skúlason.