Hi, you can bring winter clothing with you, but you'd better wear lightcoat or jacket when climb the Great Wall. Mutianyu section is about 45 miles from Beijing. You can take Tour Bus 936 at Dongzhimenwai to Mutianyu Great Wall. The lowest temperature at night in Beijing may be under zero during that time. You can find a Kung Fu School at Huilongguan, Xisanqi, Dewai. Subway line 13 can take you from Dongzhimen to get to the school.