On February 16 1998, the music video for Frozen premiered on MTV at 4 p.m. Directed by Chris Cunningham, the video was filmed in the Mojave Desert in California from January 7th to 10th.

Initially Madonna had considered filming the video in Iceland but decided that a barren desert would create a similarly desolate backdrop, without the added difficulty of filming in extreme cold temperatures. As it turned out, filming in the desert at dusk in January was far from the warm location she had envisioned; low temperatures and an accompanying rainstorm left much of the crew under the weather.

In an interview with MTV News, Cunningham stated that Madonna became interested to work with him after seeing his Aphex Twin-directed music video, “Come to Daddy” (1997). The black goth gown outfit Madonna wears in the video was designed by Olivier Theyskens, and provided by then-new collaborator, designer Arianne Phillips.