Now I'm confused - there appear to be two different but VERY similar games out.
One is called Princess on Ice:
The other is called Imagine Figure Skater:
Because these 'girly' games tend to fall under the radar of game review sites, I can't find any information to indicate if there's a relationship between them (both ported from the same Japanese company or anything) or any direct comparison of which is better.
From watching youtube, the Imagine one has REALLY annoying voiceovers, and the Princess one has prettier symbols for the rhythm-based parts... Also, the Princess one may only be available in Europe? However, it sounds like the Imagine one is still generally a better game.
Imagine Figure Skater
Princess on Ice
Links to more figure skating games here.