Snow may well feature as part of your trip, I would actively expect it in Nikko and perhaps rural areas such as around Fuji San. As well as that, you’ll need apparel that can accommodate very cold mornings/evenings and potentially warm days.

Biggest challenge first half of March is the struggle to travel “light” whilst being prepared for 4C to 16C (40F to 60F) temperatures that can feel colder (ice/sleet) and warmer (skin blistering sun) than what is being announced by the thermometer.
A child may need less volume in clothing than an adult, but not less actual pieces. They rack up. Alarmingly.

When I packed for 2.5yo LapToddler for those first three weeks in March I failed miserably to keep any semblance of order, and that was without much travelling - we had a base in Tokyo where we could keep everything. I vowed never to get so overwhelmed again and became a fully indoctrinated convert to the packing cube cult. Packing cubes are outstandingly effective with keeping tiny clothes organised.
If you do forget something, Uniqlo have a very affordable range of clothing for kids. But bear in mind that general children’s clothing stores and departments will have their Spring Summer range out. Winter gear, outside of a rogue bargain bin, can be rather harder to find.