Let me know if you need any more details at any point.

We have family based up near Sendai so, as my daughter and I have British passports (her father and grandfather do not), we have been elegible for JR East passes which have given us, not literally but in a practical sense, the equivalent to Tokyo Wide Passes. Over the past decade, figuring out worthwhile excursions has become a habit.

You’d be at the end of the season for the snow day at Gala Yuzawa, there are affordable hire items (like boots and gloves - although the gloves you keep) but there will still be plenty to see and do there and as an excursion it is straightforward and not particularly demanding. My warning to you is to make sure you are aware of the time the final shinkansen returns to Tokyo, it’s not that late. Can be tricky staying aware of the time when you’re in the pools (Spa Gala No Yu) and changing areas.
My daughter used to like getting off at Takasaki and choosing a random shinkansen to return to Tokyo on. Am not 100% sure that is still possible as I’ve seen that certain routes have become reserved seating only.