Is it recommend to go Nikko in Mid Dec?

What is the weather in December and what to expect since is a wet month.

Cold and wet

It's not wet at all! One of the sunniest times of the year!

In my opinion, winter is a great time to visit the shrines and temples of Nikko because the weather tends to be very sunny (although cold) and the shrines are surrounded mostly by evergreen trees, so it does not feel too barren.

However, the Okunikko region feels rather barren in December, which I personally do not find too attractive. There may or may not be any snow.

In other words: great for seeing the shrines and temples in the town area; not so great for seeing the nature in the national park area.

Yep - December is the driest month in Nikko.

https://weather-and-climate.com/average-monthly-precipitation-Rainfall...

Expect to have a couple of cobalt blue sky days, along with some cloud.

As Nikko is known as the freezer of Kanto, do rug up and expect the weather to change unexpectantly (will probably be mentioned on weather sites).

I also agree on it's a good time to visit the shrines, but not so much the nature part of Nikko.

It's not a bad time to visit. And not wet.
Of course, even if it were, it's still better than never visiting at all.