Hi,i'm Zhang and i'm local person ,born and bred here,,if you came at the end of Dec,,by my experiences,i got to say the weather will be freezing cold and dry then,the all day temperature gona be 5°C to -10°C..so heavy cloths and lotion are necessary.

Hi, my name is Linda,I am a Beijing English Tour guide.Now I tell you the main scenic spots in Beijing are:
1.The Tian'an men square
2.The forbidden city
3.The Temple of Heaven
4.The Ming Tombs--often for Dingling
5.The Summer palace
6.The Great Wall
7.Visit Beijing Hutong by tricycle.
If you are interest in Cultural art of China,you also could watch Peking Opera and The performs of Chinese Kufu and so on.
If there is not snow,you could go visit all the scenic spots during you are in Beijing.You couldn't go to Great Wall and Ming Tomb if snows.
Another thing,at that time it's very cold in Beijing,Please carry warmer clothes!