Christmas is 圣诞/聖誕, so when you greet someone “Merry Christmas” you say 圣诞快乐/聖誕快樂 meaning Happy Christmas.
Santa Claus/Father Christmas is known as 圣诞老人/聖誕老人, which literally means Christmas Old Man. As for Mrs Claus, 圣诞老太太/聖誕老太太 means Mrs Christmas or Christmas Old Lady.
The diligent elves are 圣诞精灵/聖誕精靈.(Remember there are no singular/plural in Chinese).
The beautiful Christmas tree is 圣诞树 /聖誕樹 . The stocking is 圣诞袜/聖誕襪. And so on. I think you get the idea? Just put 圣诞/聖誕 before a noun and it becomes Christmas related!
Another key term to note is snow 雪. Christmas is great, but a White Christmas is the best kind of Christmas. Beautiful white flakes falling from the sky gently, and ever so softly…until at last the whole place is a winter wonderland.
Snowflakes are 雪花, meaning snow flower. The sled is 雪橇, a snow sled. And a snowman is 雪人. Fairly straightforward, isn’t it?
And for all other jolly Christmas terms, I have listed them all down here to help you learn them all!