All Japanese mountain streams are closed aka no fishing from October 1st until February 28/29 every year. Some streams (there are a few in the Tanzawa Mountains) are open till October 15th while some (like Oshino) don’t open until the second week of March.
There are a few options though if you want to fish in the off season as there are numerous “fish farms” that are open year around and stocked with hundreds if not thousands of fish (like this one). However, you typically have to pay upwards of $35 a day to fish at these places.
If you are unsure of where to buy a fishing ticket you can often times by them directly from a co-op member, when they come to check your ticket, on the river. Make sure you bring plenty of yen as they almost never accept credit cards or any other currency. You still have to buy a ticket even if you release everything you catch or if you get skunked. There are no exceptions to this rule.
Also warm water rivers that aren’t able to support trout due to water temperature, pollution, habitat decimation, etc… can be fished year around. I’ve seen anglers on the Tama River and the Sagami River during the long cold winter months when the mountain streams are closed. The fish in these types of river tend to be bass, carp, and zatsugyo.