The Merry Mysteries content is only available when your system date is between 22 December and 5 January. During this time, the castle will be filled with Christmas decorations and the like. In all, it's quite similar to the Halloween content as there are 2 achievements. One of these involves finding all 11 letters to Santa scattered throughout all parts of the castle (as with finding the jack-o-lanterns). The other involves opening a gift package with a combination lock based on clues picked up in all areas of the castle.

The Merry Mysteries achievements can be accomplished in a new game or in an old, complete save. I recommend the latter because you can move to all locations easily.

For this achievement, you must find 11 letters to Santa written by the children. These look like old-school US airmail envelopes (rectangular, off-white, with a red/blue dashed border). On the face of each is a hand-written "Santa Claus, North Pole". These letters are strewn around the castles as follows:

INTRODUCTION
1 letter here, and it gives you your clearest view of them, so you know what to look for later.

• Outside the castle In your briefcase in the boat

CHAPTER 1 (ground floor)
There are 3 letters in this area.

• Main entry hall On the pile of packages under the Christmas tree
  
• Upstairs, left side On a desk in the secret "gargoyle" room
  
• Rear rooms through green door On floor under dining room table

CHAPTER 2 (living quarters)
There are 3 letters in this area.

• Bedroom hallway Rear part of hall, behind sideboard across from kids' room
  
• Mom's bedroom On top of the wardrobe where many other items are hidden
  
• Uncle's bedroom In the secret crawlspace in the wall by the computer

CHAPTER 3 (laboratory/observatory)
There are 3 letters in this area.

• Main "hub" room On the pile of packages next to the statue
  
• Hall of the Busts On table in second part of hall only accessible after entering and leaving room at far end of hall
  
• Secret store room On the shelf you're able to zoom in on

EPILOGUE (final rooms)
There is 1 letter here.

• Collections room On the stand behind the photo albums

GENERAL INFO
In the kids' bedroom, at the foot of the further bed, is a large present box with a combination lock. You must open this box to gain this achievement, and also see what the present inside is.

The lock has 3 identical tumblers, each of which has 10 different Christmas-related icons. These are a snowflake, a deer, a snowman, a teddy bear, a ski hat, a Christmas tree, bells, a candy cane, a gingerbread man, and a sleigh. To open the lock, simply turn the tumblers so that they show the correct sequence of icons. The puzzle is to figure out this sequence of icons.

NOTE: This puzzle's general idea is very similar to others in the game (and the Halloween content) so those familiar with the game should have little difficulty with understanding what is needed. The main trick is finding the clues, some of which require a rather diligent search.

Hint 1
There are 3 tumblers.
This implies that there is 1 clue in each of the 3 main chapters/floors of the castle

Hint 2
The icons are all Christmas-related things
The whole castle is littered with Christmas-related objects, some of which are icons on the tumblers. However, most such things are small and appear many times on all levels of the castle. Each level, though, has 1 main Christmas-related object that's much larger than the others and is unique to that level. Those are what you're looking for

Hint 3
Chapter 1 Location: Main entry hall.
Chapter 1 Answer: Christmas tree

Hint 4:
Chapter 2 Location: Bathroom attic
Chapter 2 Answer: Sleigh

Hint 5
Chapter 3 Location: Secret store room
Chapter 3 Answer: Snowman

FULL SOLUTION
Christmas tree, sleigh, snowman

I leave the identity of the present in the box for the reader to discover :)