i hope to visit Beijing in December 2014, does it snow at this time

Based on the weather records in the past years, it snows a little (even no snowfall) during Dec. Therefore, you don't need to worry about the road closure, which will hardly happen.

From the airport to your hotel: take Airport Express to Dongzhimen, where transfer to subway line 2 and get off at Jianguomen. After that, you should transfer to line 1 and get off at Wangfjing station (exit A) or Dongdan (exit A). Then you can easily find your hotel.

You may refer to the directions to these places from your hotel:
1. At Wangfujing station, take subway line 1 to Fuxingmen, where transfer to line 2 and get off at Xizhimen. Then walk to BJ North Railway Station to take a train to Badaling directly.
2. To Bird Nest and Water Cube: bus is a better choice. Walk to Nanyanhe bus stop to take bus no. 82 to the Bird Nest. The Water Cube is within walking distance.
3. To Summer Palace: take subway line 1 to Xidan and transfer to line 4 and get off at Beigongmen. Walk to the Summer Palace when getting out from exit A1.
4. To Silk Market: take subway line 1 and get off at Jianguomen. Leave through exit B and you can walk there easily.
May help!

1. It snows very little in Dec. in these years.
2. the road to Badaling Great Wall wouldn’t close, you can go there. Don’t worry.
3. from the airport to the hotel: you can take the airport express to Dongzhimen, transfer to subway line 2 to Jianguomen, and then take line 1 to Wangfujing, get off from exit A, northeast. Walk to the northeast to your hotel.
4. If you mean the train from your hotel to those places, then
(1) To Badaling: You can take S train from BJ north railway station to Badaling. Take subway line 1 from Wangfujing to Fuxingmen, transfer to line 2 and get off at Xizhimen. walk to the northwest you can reach BJ North Railway Station, where there are trains to Badaling.
(2) To Birds Nest: take subway line 5 to East Datun Road, transfer to bus no 538 and get off at the East of the National Stadium (the Birds Nest).
(3) To the Cube: if you go to the Cube after you go the Birds Nest, you can just walk to reach there.
(4) To Summer Palace Gardens: take subway line 1 from Wangfujing to Xidan, transfer to line 4 to Beigongmen, get off from exit A1, northwest. Walk to the west to reach there.
(5) To Silk Market: take subway line 1 and get off at Jianguomen, exit B, northeast.

Have fun there!