would the weather be too low for a 12 years old kid in Beijing from december 19 to 22?

Yes, you are right with the temp to some extent. According to the records in the past years, the lowest temperature during that period shall be around -10℃ and the highest reaches around 3℃.

As the Great Wall is in the suburb, the temp may fall to -15℃. But it is fine to take your 12-year-old kid to travel then. Just prepare quality gloves and scarves, down jackets and boots. Everything will go fine. There is heating system indoors!