Going to Karizawa in Dec 2019. We will have JR passes and will be seeing Karizawa whilst travelling from Nozawa Onsen to Osaka.
There is 5 of us travelling together.
As well as the historic town we wish to see the stone church (Karuizawa Kogen Church), Shiraito Waterfall and possibly Uni Pass lookout.
Obvously it is winter. Just checking hiring a car is possible and a reasonable way of getting to the church and the falls in a day.
I will have an interational license and drive in the snow (sludge) here in Australia.
You can rent a car to visit the church, Shiraito Falls, and Usui Pass Lookout in one day. The roads will not be closed despite the winter season, and Karuizawa doesn’t usually have heavy snowfall. Toyota Rent a Car has a location in Karuizawa, as well as many other areas around the prefecture (see here).
I believe the stone church is called Ishi no Kyokai (石の教会) and is located just 5 minutes by taxi from Naka-Karuizawa Station (see in Google Maps). The church is open for inspection from 9:00 to 18:00 on Mondays to Thursdays, but only from 7:30 to 8:30 on Fridays, weekends, and holidays. The church may also be closed for wedding ceremonies.
I hope that helps answer your question!