Well other than not being warm Beijing has tons to do and see. (Great wall, forbidden city, temple of heaven, acrobatic shows, beijing duck restaurants, hutong tours, amazing architecture). I was there 2 weeks ago and it was -5 degrees, which is the perfect winter temperature for me (I prefer -5 to +25). Beijing or Xian are the culture capitals of China. I did a tour package through Xanadu for 3 nights including all food, hotel and flights and it was 700 000. I've only done Beijing and that was because for me, going to the great wall was a must-do before I die and it lived up to the hype for me. Xian is supposed to be really great too. But if weather is that important thanI guess you're better off somewhere else.
The flights I've looked into for Hong Kong and Philippines have been jacked up so high because of the holiday so Beijing would be the same I'm guessing. Good luck.