Family trip to Tokyo

Hello guys, I'm planning a family trip from 23th of December to the 3rd of January. It's a family tradition to celebrate christmas and the new year abroad. I've already been to Japan, but not in winter, so I don't know excatly what to expect. Both me and my family like historical sites and nature. I was thinking of doing day trips from Tokyo to Nikko, Hakone, Kamakura and Izu Peninsula.

*I would be interested to know how are these places in winter?

*Are there any special places to visit only in winter near Tokyo?

*Also we would be intersted to celebrate new year in a buddhist temple. Maybe you have some recommendations what is the best place to do it?

*And my last quastion would be, how is the weather during that time? I know it's cold, but can we expect snow in Tokyo?

Tokyo to Nikko, Hakone, Kamakura and Izu Peninsula.
*I would be interested to know how are these places in winter?

Cold, but not likely to have snow in Tokyo, Kamakura and Izu Peninsula. I would also think that snow in Hakone is unlikely. In Nikko it might be on the mountains, but I was never there in winter.

*Are there any special places to visit only in winter near Tokyo?
Shrines the first days of the new year as it is Hatsumode. https://en.wikipedia.org/wiki/Hatsum%C5%8Dde
There are also some light up events in central Tokyo, e.g. Tokyo midtown, but nothing terribly spectacular.

*And my last quastion would be, how is the weather during that time? I know it's cold, but can we expect snow in Tokyo?
No, very unlikely but not completely impossible. We had a day (well, more like a morning) of snow one of the first days of last year. But it's more a nuisance for transport than anything to look for.

The only other thing to say is that many attractions will be closed over the year end/new year period. So before going anywhere, check if the place is open. Also if you plan any long distance trips, e.g. Kyoto, be aware that this is high travel season and tickets can be hard to find on some days. But I think from the list of cities you sent you should be fine, as there are non-reserved trains to all these locations.

If you want to experience snow, then you would need to go to the Japanese Alps. In shinkansen actually not too far away from Tokyo.

Enjoy your trip to Japan!