In November, Beijing has both feet more or less in winter. The heating goes on from mid-November as things can drop below freezing.
Heating is normally provided from November 15 in hotels as the temperature may drop down below freezing. It’s certainly jacket, gloves and hat time. There are strong winds sometimes but little rain or snow. Hotel prices drop substantially.
November is cold in Shanghai and bitter winds can blow. There is low rainfall but it can be foggy. Low season prices kick in.