I'm gonna stay at my host family's house in December, which is gonna be really meaningful for me because they always take me to different places and teach me lots of informative things. teach me about local culture.

This sounds more natural, but not sure if it exactly what you were thinking.

The Winter Break

Yesterday,I finished my exams and my winter break finally starts today!
I was so busy with exams and presentations these last two weeks, but now that I have one month off, I'm so excited :) I'm gonnaing to ["gonna" is an informal abbreviation, and shouldn't be used in writing] stay at my host family's house in December, which is gonnaing to be really meaningful for me because they always take me to different places and teach me lots of informative [this is technically correct, but sounds a bit awkward] things.
The goals for this winter break are talking with many people, reading a book [only one?],and practicing the violin.

Good night !

Nice job!

The Winter Break

Yesterday,I finished/completed my exams and my winter break finally starts today!
I was so busy with exams and presentations the/ for the/ during the last two weeks, but now that I have one month off, I'm so excited :) I'm gonna stay at my host family's house/ I'm going to stay with my host family in December, which is gonna be really meaningful for me because they always take me to different places and teach me lots of informative things.
The goals for this winter break are talking with many people, reading a book,and practicing the violin/ The goals for this winter break are to talk with many people, read a book and practice the violin. 

Good night!

Well written! I was not sure if the last sentece was gramatically incorrect so rather than crossing it out, I wrote what I would have said. I hope that you enjoy your break! :-)