I am visiting Shanghai in mid January. What is weather like during that time period?

The temperature might differ from 40F to 50F in a day. It might drizzle sometimes, but it won't influence your visiting too much. Enjoy your time there!

Am here already in the city, very mild and been raining since I got here 2 days ago. Locals are saying this is a warm winter. Its 50 degrees F as of this jan 7 date

it is going to be cooled in January and feb. From the month March it will be the best time to visit.

I am staying here since 24th Dec 2017. as am an Indian I feel this weather is very cold to me as it dwells from -5 deg to maximum 10deg. But when I see upcoming forecast, its showing the temperatures are going to fall down much more till end of January and later it starts raising till September (which is peak summer season). So be ready to face -5deg to +10deg temperature with warm clothes & sweaters. preferably wear thermals inside.