Karuizawa in December

Hi! We’re planning to go on a day trip from Nagano to Karuizawa around Christmas time. Since we only have a day, was wondering which attractions are actually worth it.

We’ll be starting at Karuizawa Station so places like Kumoba Pond, Kyu-Karuizawa Ginza, and Prince Shopping Plaza are nearer. Should we stick to these places or is it worth opting for Shiraito Falls and Harunire Terrace, which are at the other side, instead?

Also, does it snow in these areas around Dec 20 onwards?

Thank you!