I plan to visit beijing in late december.

Yes, you can visit at that time. Actually these two places are quite near the city, both of them can be reached by bullet trains.

From BJ Railway Station, you can take the bullet trains to Shanhaiguan railway station. The duration is about 2.5 – 3 hours. And the fare is about CNY92.5 for the second class seat and CNY110.5 for the first class seat. Upon arrival at the train station, you can take the tourist bus line 4 or line 5 to the pass directly.

From the south railway station, there are a lot of trains to Tianjin. The duration is about 33 mins, and the fare is CNY54.5 for the second class seat and CNY65.5 for the first class seat.