She is leaving him because...well, it started saying that he does not earn enough for the life style she would like to have (she is an accountant in the city but he is not - despite he has a decent job, he earns less than her). Now, she says that they are different.
You are hearing 1 side of this story. Support your male friend, but have you considered that her side of the story is "my husband is feckless with money and relies on me to keep bailing him out?" or "my husband talks talks talks about career plans and strings me along with tales of gardens for our little one, but only works 16 hours a week in a dead end job he says he hates but really is cruising in"?
Your version of the story is at one extreme.. my words above are at the other end.. the truth's somewhere in the middle probably.
You do NOT know this relationship. You only know what you've been told.
overall because they have a 20 months old daughter and he will miss her.
Well, obviously
Any relationship breakdown is upsetting.
Anyway, the mother has now decided to spend christmas day with friends
Well, yes, since they're separated, do you not think it would be strange and confusing for everyone if they spent Christmas together as if all were as usual? 
the little girl and the father will go to his parents as every year to celebrate with the family.
Excellent, little one gets to see her dad and grandparents - what's bad about that?
My friend is upset that his exwife prefer to go to the friends and leave the young girl behind for few nights.
Er, they're separated.
The little one's mother has agreed with the dad to let the little girl stay with him and visit nana/grand papa. What's bad about that?
Is it that you disapprove of her not playing wife to your male friend? Do you not think that would be confusing (not least to the little one!) and .. well... strange?
I am shocked she is leaving the daughter in this way. AIBU?
Yes. VERY. None of your business. And the snippets of info you have are a one-sided story.
Tell me, is it this woman specifically that you disapprove of, or do you think all separated parents (or even divorced onces) should put on a lie at Christmas and play happy families, even if that ultimately confuses the children?