It's called "Fire & Ice" and has gorgeous sets, costumes and scenery for both the Fire land and the Ice land (in which most of the story takes place) as well as a lot of inventive and beautiful choreography. While it isn't specifically about Christmas it definitely has that seasonal feel- music included. I don't think it was out of convenience or by coincidence that saw this film originally have a Christmas release.I'm positive I've read fairy tales similar to this (Japanese? Russian?) but time is against me to research this properly. If you know of any tales please do add a comment with the title and/or link.
Here's a story description of "Fire & Ice" from Wikipedia:
Fire and Ice is a full length company piece creating narrative ballet on ice. Set between the Planet of Fire and the Planet of Ice, it tells of a love story between a Prince of Fire and a Princess of Ice. It is a full set piece with visual designs and effects depicting different locations on the two planets and telling the story.
The piece opens with Dean performing actually ballet within the catacombs of the Plant of Fire, while seeing Torvill in the blue flames of their alter. Upon diving in he finds himself upon her planet. He meets her, and after taking some time to adapt to her planet, they fall in love. She gets called away to a Royal Ceremony but she rejoins him later. The following morning they are discovered and a violent attack is carried out on the Fire Prince by her own people. She pleads with her father to have mercy on him but he banishes her from his sight and the Fire Prince is left trapped in a prison of ice. Later the Ice Princess sneaks back to him and melts the ice with all her strength, leaving her close to death. The Fire Prince revives her and they are together once more. Meanwhile the Prince’s own people have witnessed his fate in the flames and have arrived on the Planet of Ice. A war breaks out which ends in the death of both the Prince’s and Princess’s fathers. Devastated and alone, they find each other once more and grieve. As time heals their wounds and their love endures a distant archway appears, touring over the icy mountains. We watch them make their journey towards the arch and finally enter and make their break for freedom and a new life together.
Torvill and Dean devised Fire and Ice in Australia with Graeme Murphy, sold it to LWT (London Weekend Television – part of ITV). It was written by Tom Gutteridge and Carl Davis and rehearsed and filmed in Germany ready for its UK television premier in Christmas 1986.You can find out more about the production HERE and occasionally DVDs surface like the one below and become available to own (yay!). I gather it's also available on the 'Dancing On Ice' DVD from 2006.Some lovely person put up the whole ice-ballet on YouTube (in 19 very short parts - between 30 seconds and 5 minutes each) and I've made a playlist so you can press "go" and watch them all automatically play in order. Just press play.