You can actually get the ideas from a situation, trend, and literary work. For instance, you sort of paraphrase your friends' letters of Merry Christmas from last year. There are a lot of funny stories in magazines regarding Christmas, including Merry Christmas letters. You can be more humorous too. Also, you can get the ideas for the letters from Christmas novels and movies. Looking at signs you see on the street is another option to get inspiration if there is nothing left on the internet.
You should make Merry Christmas for letters because you have to spread happiness around the holiday. Especially, when you send the letters formally to your boss or headmaster, you should mention Merry Christmas and another message you can write to say thank you and any friendly manner. It goes the same with your best friends and family. The letters of Merry Christmas is just to give them some gratitude during the year and wishing them more joyful days in the next year.
Yes, there are formats to write Merry Christmas for letters. You have the freedom to choose whether you want to follow the format or not. You can be a bit poetic for the letters in the Merry Christmas card or any greetings you make. If you want to send the letters to your closest friends, roommates, and classmates, you can use the bullet format. You can write like thanks for taking care of yourself, washing the dishes, doing the homework together, etc. The format still keeps the traditional one too. You can still write "Merry Christmas" or use a card with the writing of it on the cover. It is simpler, isn't it?
You can describe the holiday, instead, like "In this holiday season, let us merry ourselves with sweets." You can also write situational yet fun words, such as "Merry Christmas! May the day make you fully happy as you're tummy filled with foods." For your distant family, you can write "Merry Christmas! I hope your family is all as active as robots." Saying "Wishing you all the merriest Christmas" is also acceptable for both formal and informal letters. You can say a prayer as in "Hope this Christmas fills with joy and peace."