Hi Is there any place near Beijing we can visit to see great snow? My 5 year old twins have never seen snow before.

If it snows, the best place to see the scenery are the Forbidden City and the Summer Palace. But it is not sure whether it will snow or not during this year's Christmas.
Usually, the December is the snowing season, but it is not alway snow in that city.
If you have enough time in China and want to enjoy the snow scenery very much, it is suggested to fly to Harbin or take bullet trains for Harbin. It is the paradise for enjoying snow scenery. Christmas is always the opening time for local Ice and Snow Festival. I am sure you and your childern will be impressive.

Harbin is great, but I guess it wouldn't be a day trip from BJ. How about Nanshan ski area?

Yeah, Harbin seems a little far away, but Nanshan Ski Resort would be a good choice for snow for sure. To get there, direct shuttle buses are available and you can take that at Sanyuanqiao/Wudaokou at 08:30 every morning. It requires reservation one day ahead and the hotline is 010-89091909.