I will go to Shangri-la on December 8 or 9 and then will go to Diqing.

But SL actually belongs Diqing. I wonder if you refer to Deqin. If so, it is 5-6 hours' driving distance way. So yes, when it snows heavily, the roads between the two places may be closed. But as I know, it usually snows lightly in early Dec. so no need to worry much about that. Just pay attention to the weather forecast before leaving in case.