I plan to go to Shangrila and Lijiang in December 15 to 20. What is the weather like at that time.

Most of time then will be fine, but you may feel a bit cold. The average temp then will be 5-6C. And sometimes, the lowest temp can fall to -3C. So you need take one or two warm clothes. Relatively, Shangri-la is colder than Lijiang, so you'd better pay attention to the weather forecast at that time.