My family will be visiting Beijing by this coming Mid Dec.17.

As I can see, the snowfall is a little hard to see in the city, so you can pay a visti to cities furthur north, like Harbin.
By the way, the flight to Harbin takes less than 2 hours.

For the attractions, I’d like to give you some advice.
Day1: after you have a rest, you can wander around Wangfujing Street.
Day2: pay a visit to Badaling Great Wall and Ming Tombs. Take Bus 877 from Deshengmen to the wall, and then change bus 879 to the tomb.
Day3: Tian’anmen Square- Forbidden City- National Museum
Day4: Beihai Park- Shichahai Area– Hutong Tour