I’m not sure why it should be, but my two favourite indie Christmas songs are both from Swedish bands. One, by the Hives, is coming up on Tuesday but today’s comes from Hello Saferide. I don’t think it’s available anymore (depending on what this page says) but you can pick it up from a few blogs like this one.
The chords don’t work perfectly on the uke. You could switch it up a semitone so that:
A = Bb
C#m = Dm
Bm = Cm
E = F
But I think it sounds better in the original key.
Just down strums will do for the first part and this will get you through the rest of the verses:
d – d u – u d –
In the chorus go with two down-strums each for the Bm – E move.