Do you think Zoey should have told her friends about the way she wanted her birthday to be?

Zoey acted terrible in this regard. All of her friends knew the date of her birthday, meaning the topic must have come up before and there is no reason why she would not have told them at the time how much it displeases her that she always gets christmas presents. There is basically no level of trust needed to tell them that. And while Stevie Rae was her best friend Zoey permanently says how close she is with all her friends meaning she should have a bond strong enough to tell them something like this.
Plus, at the time it would not have hurt anyones feelings, because her friends would not have bought something like a crhistmas present for her birthday before knowing that her birthday was on christmas.
However, Zoey does not admit to herself or anyone that she is atleast partially responsible. Instead she tells them how she told it to Stevie Rae and makes everyone feel miserable for calling her out on it.
Its even worse because in the context it clearly looks like she is doing it on purpose. Using a dead friend just to win an argument would simply be unforgivable.

I never considered how her friends knew the date of her birthday without conversing her. However, they might have learnt about it from another source or they had only touched on it briefly and Zoey never took the time with the group to have a longer conversation about it, whereas with her roommate she has plenty of time every evening and morning to discuss whatever.

Zoey doesn't appear to have any fond birthday/Christmas memories, she certainly never touches on any during the books and since her best friend did die (or was perceived to) less than a month prior, so I'm not surprised that topic might not have come up before everyone bought their presents. Zoey certainly had more important things to occupy her mind: an undead best friend, an evil mentor, a jealous boyfriend, a clingy ex-boyfriend, a seductive teacher, Dark Daughter duties, and homework.

Personally, I put all the blame on her friends because I just don't understand why anyone would think those "Birthmas" themed presents were a good idea.

I will not argue that stuff like seemingly expensive boots with christmas motives are a bad presents. As a non american I actually assumed this was somewhat typical for the US, because the text seemed to imply, that they were completely acceptable and typical for christmas presents.

But the entire book is pretty much madeup of Zoeys thoughts and at the time she is only pissed at her friends and tells the reader how she is not responsible. Usually we're presented with every tiny thought Zoey has, therefore the absence of such a thought does not make it look like that was the reasoning behind it.
If she would get her presents and only then remembers that she never told her friends about her issues with christmas presents, I would agree with your interpretation.

And even if it was she still actively blames them for doing something wrong despite never telling them otherwise. I do give her credit for not saying it out loud, but at the same time I have to wonder how you can get angry about something like that, if you are confronted with so much bigger issues.
I could accept it as just letting her anger out on her friends over triviality, because she is confronted with so many more crucial matters already, but again there never is the realization that she might have overreacted or gotten angry over something completely different.
The others are all supposed to be close friends, but they never communicate about misunderstandings like this and apologizes are practically never made by Zoey and rarely by anyone else.