Which schools are you applying at? If you have been applying for jobs at private schools/training centres, yes they will be very vague, they will mess you around and waste your time.

Better to apply at public universities. Now is a good time, they will be looking for new teachers for next year ( next semester ) late February, early March. Spring Festival is January 30, so, classes begin a few weeks later from then.

You have a BA, so why even bother applying for jobs at training schools? Ask the university to send you the documentation to apply for your Chinese Z-visa in your home country. It is not that difficult.

As for weather, Guangdong and Guangxi provinces are warm most of the time, but both provinces can be quite cold from the start of December till the middle of February.

Nanning for example had a very cold winter in early 2011, also in 2012, it lasted till the middle of March. So don't listen to people who say southern China is always warm, it is not true.