The accompanying music video for "Frozen", directed by Chris Cunningham, was filmed at Cuddeback Lake in California, and features Madonna as an ethereal, witch-like, melancholy persona, who shapeshifts into a flock of birds and a black dog.

To promote Ray of Light, Madonna performed the song live in several occasions, including its first world premiere on Sanremo Music Festival in Italy and on Wetten, dass..?

By the mid to late 1990s, Madonna was in a more mature and introspective mood, after giving birth to her daughter Lourdes, gaining interest in Eastern mysticism and Kabbalah, and earning the title role of Eva Perón in the film adaptation of the musical Evita (1996).

In 1997, Madonna began working on Ray of Light, her seventh studio album and wrote songs with William Orbit, Patrick Leonard, Rick Nowels and Babyface.

Author Carol Benson noted that it was a "deeply spiritual dance record", with the crux of it based on Madonna's career, her journey and the many identities she had assumed over the years.

[1] The singer drew inspiration from Bernardo Bertolucci's 1990 British-Italian drama film, The Sheltering Sky, which dealt with a couple trying to save their marriage during a trip to Africa.

[12] Tom Ewing of Freaky Trigger described Orbit's drum and electronic programming as "extraordinarily abstract for a global smash – a kind of cold, bassless dub approach, where the gaps, echoes and drop-outs matter as much as the beats, which spread sharply, like sudden cracks on a frozen surface.

Sal Cinquemani of Slant Magazine complimented the track's production and deemed it "one of the great pop masterpieces of the late 1990s", adding "Its lyrics are uncomplicated but its statement is grand.

[21] In a separate review, Larry Flick called it a "stunning foray into the realm of electronica [which] [...] underground purists and unwavering popstars will equally applaud".

[25] Joan Anderman from The Boston Globe said that on Ray of Light, only "Frozen" achieves a "state of divine balladry", recalls the "emotional pitch" and simmers the "beauty of 1986's 'Live to Tell' with a dark, lush string section, the smash and patter of a lone drum, and an ominous, pulsing buzz".

[28] Elysa Gardner, writing in the Los Angeles Times, said "Madonna's enduring knack for incorporating hip and exotic textures into accessible pop tunes is evident on the plaintive single 'Frozen'".

"[31] Also from Entertainment Weekly, Chuck Arnold wrote: "sounding unlike anything Madonna had ever done before, and creating a mystical forest of sonic wonder — sweeping strings and all — 'Frozen' possesses an almost operatic grandeur that never fails to give you chills".

'Frozen' marries the different temperatures of 90s pop stunningly – the faltering chill of William Orbit's electronica with the dusty, cinematic heat of North African melodies and strings".

[50] In Canada, the song reached a peak of number two on the RPM Singles Chart in its seventh week, being held off from the top position by Natalie Imbruglia's "Torn".

[63] Directed by British artist Chris Cunningham, the music video for "Frozen" was filmed at Cuddeback Lake in the Mojave Desert in California during January 7–11, 1998.

Her form then changes to a shiny black liquid, which runs along the desert floor and appears to be absorbed by the tattooed hands of another version of herself, curled up on the crenellated ground.

[74] He concluded that the viewers find themselves in control of their view, of the situation in general, and are conveyed the impression to follow a realistic depiction of a mere melancholic woman in the desert, according to him.

[74] Henry Keazor and Thorsten Wübbena of Rewind, Play, Fast Forward: The Past, Present and Future of the Music Video said that the large panels of cloth that gather and wind around Madonna gain an even more obvious independent movement quality.

[96] Shaad D'Souza of The Fader and Sebas Alonso of Jenesaispop criticized Madonna for releasing too many renditions of the remix, the former's problem was over-promotion, while the latter's point was that they were short.

Writing for Variety, Mike Wass commented that Fireboy DML "laments over Sickick's sweeping trap beats" and takes the song to "soulful direction, plunging deeper into heartbreak territory".

[79] George Griffiths of Official Charts Company called the rendition "TikTok friendly" and additionally wrote: "The song morphs from Madonna's ice-cold, electronica-influenced vocals, shifting into something of trap beat for Fireboy DML's verse.

[96] Jenesaispop's Iker Oroz called this remix "insubstantial"[104] while Sebas Alonso writing for the same publication, opined that the performers are lacking chemistry on the track.

[82] Yohann Ruelle of Pure Charts opined that the clip is "hot";[110] whilst Jenesaispop writers were not keen of the video, describing it as "insubstantial" and "not difficult".

[116] The first verse of "Frozen on Fire" makes reference to Sickick "popping Molly", a seemingly subtle nod to Madonna's twelfth studio album, MDNA (2012).

"[97] "Frozen on Fire" was released on May 19, 2022, for digital download and streaming through Warner Records and Artist Partner Group,[101] whereas the song was sent to Italian radio airplay next day.

[121] On April 29, 1998, Madonna made an unannounced appearance at the 9th annual Rainforest Foundation Benefit Concert at New York City's Carnegie Hall, where she performed "Frozen" with the East Harlem Violin Project, while wearing a Versace dress.

[127] For the second European leg of Madonna's Sticky & Sweet Tour in 2009, the performance of "Hung Up" was removed from the setlist and was replaced by an up-beat version of "Frozen".

"[135] Polish industrial metal band Thy Disease used parts of the original strings and vocals in a cover on their 2001 album, Devilsh Act of Creation.

[138] In May 2013, contestant Olympe sang the song on the second season of the French version of The Voice: la plus belle voix, allowing him to reach the show's semi-final.

[140] In November 2005, a Belgian judge in Mons ruled that the opening four-bar theme to "Frozen" was plagiarized from the song "Ma vie fout le camp" ("My Life's Getting Nowhere"), composed by Salvatore Acquaviva.