Hi, It is very cold at that time. The usual temperature is about -10~1℃。 Snow may fall at that time. Well, you can still go and climb the Great Wall. You will see a distinctive flavour of the Great Wall with snow. You need to wear warn winter clothes like eiderdown outwear and warm boots. When climb the Great Wall, you need to wear warmer clothes with antiskid shoes, plus gloves and cotton-padded cap. I think you may have a view of Great Wall Hiking Tours(https://www.travelchinaguide.com/package/beijing/greatwalltours.htm) which may do benefit for you.

Thank you Mr. David for the information. Initially we were thinking about january visit, but we moved it to december 7 to 10. Is there a possibilty to see snow at that time? Our country doesn't have winter season, so we are hoping to see snow in beijing, (hoping) even at mid december. TY