Advise on 3 days itinerary in Beijing

Well, the scenic areas you mentioned above all open during that period of time. And you can still make full use of the public transportation to get to those places. So don't worry.
About the weather, the temperature is 25 F to 47 F. It's still cold. So bring boots and sneakers.

You are suggested to have a dinner at Wangfujing Avenue. There are many restaurants and local foods for you to choose. And you must to taste Roast Duck.

Both Badaling and Mutianyu are OK. But Badaling Great Wall wins higher popularity. The transportation is easily accessible. Public bus no. 919 or train can take you to there directly.

Have a good journey!

Keep in mind that if you arrive at noon it might be 3 PM by the time you check-in, you'll arrive on a holiday so traffic may not be that bad. The reason I bring this up is that parks close earlier in the winter, so you'll probably have little time to see the Summer Palace that first day. Jingshan Park, The Forbidden City and Wangfujing street are somewhat close to each other so you could go there on the same day.

As has already been mentioned, you can get to all those places easily by bus or subway. Map apps, like Google's will give you information required to get anywhere by public transportation, however, they're often blocked on China so using them requires a VPN. If you have that covered, please trust it as they're quite accurate and will save you from any chance of being scammed on your way to the Great Wall. Of course, if you know Chinese get Baidu maps, it'll work fine and provide the most accurate info. BTW you can reach Badaling by train from Beijing North Station, it comes with a bit of a walk, but it's also an option.

Sadihy,

Thank you for your advice and suggestion!
This will help me to revise my plan and have better visit in summer palace and other attractions.
Coz I just have 3 days, time is short.

Harry,

Thank you for your information! I will bring warmer clothes there and try the roast duck! Everyone said it taste good!