Ну , с началом фраз помогу, оформить придется самому. 
Dear (имя друга), 
Thank you for your gift. I really liked it. We celebrated New Year (место) 
We decorated a New Year tree with (чем именно украсили). 
My mym made (что приготовила на ужин) 
We invited (кого пригласили) 
My parents bought gifts for (для кого именно купили подарки) 
They put them under the New Year tree. 
We had a great party. 
We sang songs, danced to music, played funny games and others. 
Well, it was fun! 
How did you spend New Year Eve? Did you like it? 
Love, Oleg. 

можно начать так::

My dear friend, 
I wanted to share with you my emotions about last New Year  party but I cannot because I was so pisst that I do not remember anything. 
Do you remember my name? 
Thanks

"Hi Margaret!(Имя можно придумать свое)
I hasten to congratulate you on the New Year and wish you have a great winter vacation.
You know, I want to share with you their planami.Na winter vacation my parents are going to visit a ski base, imagine how it will be fun! And before the New Year I will go to a concert of his favorite band, my dream come true!
I'm waiting for a letter from you, I hope you can tell me how to spend the holidays.
So far, your Anna.(Имя опять таки можно придумать) "