Contrary to popular belief, when making a CGI animated film, each individual frame has to be shot just like a traditionally animated film: one at a time. The only difference is that it's the computer that takes these pictures, and each picture takes several hours to render. The simplest shots in the film (such as the end scene between Anna and Kristoff) took three hours, while the most complex (Elsa building her ice castle) took thirty hours and 4,000 computers. The animation of the film was supervised by Chris Buck; areas such as story, acting and art design were supervised by co-director Jennifer Lee, who with this film became the first female director of a Disney animated movie.
The characters in Frozen required an extensive amount of planning and animating. To capture Elsa's expressions, her animators first filmed themselves acting out her scenes, then combined their acting to create the final product. In addition, Elsa's facial expressions were modeled after Idina Menzel, her voice actress. To accomplish this, the animators filmed every recording session, pointing three cameras at her from three different angles. As well as this, Menzel's breathing was reproduced frame-for-frame onto Elsa.
To obtain a sense of hyper-realistic animation, Elsa has 420,000 hairs on her head; the average human has about 100,000. Anna's face has over 70 animation points; each point can be dragged by the animator to create expression. The most "realistic" character in the film is Hans, with about 180,000 hairs and only 50 animation points; even these are more than the average person.
New animation software was created to aid in making the film; without the new software, the final product we see could still have been accomplished, but it would have taken several extra years of planning and rendering. Among the new software created specifically for the film was a program that helped create realistic snow. A handful of snow is actually a handful of snowflakes, so it's difficult to animate all the properites of snow, especially in the same frame. A specific program called "Matterhorn" was thus created; it was used in a total of 43 scenes in the film, including all the ones where snow is shown falling or otherwise in the air.
A program called "Spaces" was invented to control Olaf's various body parts and inform the computer which snow was actual snow and which was part of Olaf. Another program, "Flourish", allowed minute details like leaves and twigs to be art-directed (in essense, animate themselves in a realistic way, given properties such as wind and gravity). "Tonic" was created to help animate various characters' hair--a process that has often been difficult in CG animation. The combination of these and upwards of 20 new programs helped to accelerate the film's progress, to the point where entire scenes could be completed within a month or less.
The "Let It Go" sequence contains elements of hand-drawn animation mixed in with CG, though these were mostly used to aid the computer in animating the scene. While the rest of the film evolved around it, Let It Go changed very little from the beginning of production, and was thus the first scene of the film to be animated. At the time, only two necessary software programs needed to aid the film had been invented, so animators had to animate most of the sequence by keyframe animation. This resulted in a different, old-school feel for this scene in particular, so while it doesn't stand out from the rest of the film, it still has an alternate feel.
Idina Menzel recorded her singing for "Let It Go" while listening to Robert Lopez and Kristen Anderson-Lopez's piano demo recording, in October 2012. The background orchestra wasn't recorded until February 2013, long after the sequence was fully animated. Menzel was told by director Jennifer Lee to imagine what was going through Elsa's head with every line of the song, but otherwise received no direction and was left free to express herself however she wanted. The final product is all from the same take (but not the first one), which is rare for a musical number.
Kristen Bell was the first actor cast in the film, in March 2012. She recorded most of her lines while pregnant with her first child; she had to re-record many of them after giving birth, in order to help Anna sound more childish than previously. Idina Menzel was cast as Elsa in June, but in actuality they both were guaranteed the roles in late 2011 at a table read. At the table read, they played off each other in a way that deeply impressed the directors, producers, and Disney executives, and when it was time to go, they stayed behind a few extra minutes to sing "Wind Beneath My Wings" together. At that point, directors Chris Buck and Jennifer Lee knew they had found their Elsa and Anna.
Josh Gad was the final actor to be cast; the announcement came in June 2013, barely five months before the film's release. Many of Olaf's scenes had already been animated, so Gad had to lip-sync to Olaf's already-animated mouth for many scenes. Some, however, were left unaminated specifically so that he could act as he wished; these included his first encounter with Anna and Kristoff, and the final scene of the film where Olaf enjoys summer.
Disney exectuvie Bob Iger confirmed in June 2014 that all information used to make Frozen (from preproduction storyboards from the 1940s to the final rendered frames of the film, and everying in-between) were safely stored in Disney's digital storage facility.