Regarding weather, it depends on how quickly and how far you head south. Beijing in November can be pretty chilly, December is downright cold. However, in the far South (Guangdong for example) it is often very pleasant up to mid-December. I would be very surprised if you experienced extreme cold in this period unless you choose to head to the far North or West of China
The weather has nothing to do particularly with solo travelling, same summer or winter. The usual rules therefore apply - make sure you can communicate, look after your belongings (although China is pretty safe in this respect) and don't leave your brain behind in UK
Trains v planes: Trains are generally quite a bit cheaper even though flights are not very expensive, particulalry if you choose the cheaper seating options. Trains are obviously slower but I find them great for seeing the country (you have plently of time) and meeting locals. Providing you can get by with your communication I would choose trains
btw....you are being a wuss

- relax and enjoy a great trip
nickyboy