As others have said OP, the couple may well have very good reasons for picking that date, family/friends already visiting for christmas just travelling a few days earlier rather than making them travel twice in one year, or it being a significant date for the couple (lots of people meet their partner at Christmas parties).
As close as your SIL seems to be, if her attendance was important to the couple, they would have asked her first.
While your SIL is having to travel, it could well be the key guests can do this in a day.
It could well be this is being used instead of a normal family meet up over the festive period.
I have never had my hair done specifically for a wedding, expect for my own. I assume your SIL has known for several months that she was invited to this wedding and could have just got her Christmas stuff done in advance.
It could well be as lovely as your SIL is, she's one of those martyr types who seem to make everything into a traumatic chore that she's just coping with and not complaining. Oh no, far too lovely to complain, just whinge about it to others, rather than just decline.
(And you can decline wedding invites that don't suit, I've turned down several over the years!)