The first Christmas special starring Matt Smith the Eleventh Doctor was written by Steven Moffat to be exceptionally Christmassy... But it also manages to be the best since The Christmas Invasion, despite being exceptionally sentimental, mostly by also being a lot of fun and imaginative.
So the Doctor's new companions are endangered while on their honeymoon... For reasons too complicated to go into here. The one man who could save them and the others soon to die alongside them is a spiteful old git played by the wonderful Michael Gambon won't lift a finger to help!
Commence operation: visit the past to change his mind! Despite that obviously being a paradox... Ah well, who cares? Christmas!
The Doctor reveals and changes elements of old Kazran's past and eventually is forced to show his younger self what his future holds before the day is saved. But the journey is far more important than the destination in this special.
The strange planet with flying fish (and sharks!) is lovely, the Dickensian story beautifully told and even though the threat seems distant (because we know the companions won't die horribly in a Christmas special), there is still a lot of investment in the featured characters of Kazran and his doomed love Abigail.
A Christmas Carol succeeds in what Moffat intended. It is very, very Christmassy. It is fun and has a simple moral message. Sure, it suffers from the Smith-era issue of everything functioning by fairy tale rules instead of any kind of logic, but for a Christmas special that hardly seems out of place.