Is it ok to bring children 2 years and my mother (60 years ) to beijing on 5 dec 2012.

It will be cold there. Recently, the temperature is around 3 to around -4C, so it will be colder then.
It is safe to climb in winter, but I do not think it is a good time to climb for 2 year old childern and old people. The Great Wall is on the mountain, so it will be much colder than the city and for them the physical strength maybe the biggest problem in the cold day. I suggest you to adjust your planning according to the weather.