When Gracie Gold announced she was skating to "Let it Go" with much fanfare in the footnote of an Icenetwork article that was about a different skater, there was an immediate storm of excitement and anticipation among figure skating fans in South Korea. After a fuzzy fancam of her performance on SOI appeared on Youtube, it immediately received hundreds of thousands of hits within the first twenty-four hours--the majority from Korea. The performance, and the song, became so wildly popularly that it retroactively was responsible for the animated film, Frozen, becoming the #1 most successful animated film in South Korea of all time, inspiring numerous covers by Korean singers that received hundreds of thousands--even millions--of views. All South Korean fans immediately became Gracie Gold fans via her moving and inspiring performance. One fan, also a Yuna Kim fan, created a Yuna Kim montage to "Let it Go," but barely anyone noticed--only 856,000 views so far (but some little website called the Hollywood Reporter took note of it). Samsung ingeniously decided to take advantage of the "Gracie Gold wave" and had Yuna Kim sing "Let it Go" to a montage of her skating--but unfortunately, since it didn't feature Gracie, it has only garnered 1.4 million views.
Hence, the decision to have Let it Go in the All That Skate show can only be attributed to Yuna seeing Gracie's SOI performance and an instantaneous reaction to copy the one and only Gracie Gold.