What to wear to the Snow Monkey Park

Feet first
The trail is 1.6 km of unpaved path each way, and from roughly December it is packed snow and ice on a slope with the steepest bit at the end. The park recommends snow boots or similar in winter and hiking shoes in summer, and it also recommends buying simple crampons in advance for a safer winter visit. Buy them before you travel rather than hoping. I have seen a great many people in city trainers on that path and none of them were enjoying it. More on the surface itself in the walk to the park.
Dress for standing still, not for walking
This is the mistake I see most. You will be warm walking uphill for half an hour and then you will stop moving for an hour at 850 m in around −10 °C. Layers you can open on the way up and close at the pool. A hat, because most of the heat goes out of the top of you while you stand watching. Gloves that come off without a struggle, plus thin liners underneath, because bare hands on a metal camera at that temperature is a short experience. See how cold it gets for the numbers.
Put spare socks in your bag. Snow gets into boot tops on the way up, and the walk back down is thirty-five minutes long with wet feet if it does.
What happens to camera lenses
Two things. Steam off the pool condenses on cold glass, so you will be wiping the front element constantly; a cloth in your pocket, not in your bag. And a cold lens brought straight into a warm bus or ryokan fogs internally and can stay fogged for a while. Put the camera in your bag before you go inside and let it warm up slowly. Batteries also drain fast in the cold, so keep a spare against your body.
Outside winter
Hiking shoes and normal walking clothes. Spring and autumn are cool in the valley even when Nagano city is mild, and summer on that path is humid work. Which season you are packing for is worth settling first — best time to visit covers what each month actually gives you.
Frequently asked questions
Do I need crampons for the Snow Monkey Park?
In winter I would wear them. The park itself recommends buying simple crampons in advance for a safer visit, because the 1.6 km trail becomes packed snow and ice. See the walk to the park for what the surface is like.
What shoes should I wear to the snow monkeys?
Snow boots or similar in winter, hiking shoes in summer — the park’s own guidance. Trainers are not adequate on an icy uphill path. How cold it gets explains why the trail behaves the way it does.
How cold will I actually be standing at the pool?
Colder than on the walk up, because you stop moving. Winter temperatures in the valley drop to around −10 °C at 850 m, so dress for an hour of standing rather than for the climb.