Hi there. I understand most cities in Northern China tend to have very hazy weather come December.

The temperature may range from 40 F to 50 F during that period of time. And there may have several cloudy and rainy days. Perhaps it will have foggy weather.
In addition, to be honest, it's not advised to tour around that mountain in the end of Dec. because the weather would be cold. And the snow days will add many difficulties to the road condition. Thus you can change your travel plan. In general, April to October is considered the best period. :)

Thank you Leo for your advice. Can only go in Dec unfortunately.