You mentioned having five days empty for leaving Tokyo, so I’ve been working with that number, but more (or less) days could be added if you want to change things around.
The first day would include your arrival to the area (around a couple hours away from Tokyo) and a visit to some of Japan’s most impressive and elaborate shrines. Hiking isn’t really an option in February so you’d have plenty of time to try out the local food. At night, you can head over to the snow festival to see the snow houses lit up.
You may want to try sleeping in a traditional ryokan or, if you’re on a tighter budget, a traditional minshuku which are more homely. The second day includes some snow scenery and a frozen waterfall before taking a countryside train to your next base.
The third day would be more of a cultural visit, including a big castle and historic samurai sites and a snow-covered hot springs to warm up. Your last two days could be a day trip to a secluded old rural town (covered in snow) and the photogenic “ice train”, as well as some hot noodles considered to be the best in Japan, before heading back to Tokyo.
Of course, this is just a first draft without knowing much about your group and interests, but if you’d be more interested in other things we could easily change them around. These places are all close together and not far from Tokyo.
But of course, one of the best things about winter is the food! Fire pits, heated kotatsu tables, hot pots and warm snacks…