What times are considered peak season

I'm trying to figure out the timing for making hotel reservations; I know for hanami, Golden Week, and maybe New Year's Eve it's better to book several months in advance, but what about for koyo (mid-late November)?

almost the whole month of november is peak season in Kyoto but especially the last 2 weeks.

Then would it be enough to reserve 3 months ahead?

I'm going to Kyoto in the last week of November, and I booked my accommodation in July...and by that time, most of the more affordable places were already booked out! You definitely want to plan ahead as much as possible. Find somewhere you want to stay well ahead of time and then just wait for their booking system to open (if it's not already).

I was able to book a late November reservation for Kyoto in late May. In mid June I found a somewhat better hotel and was able to change it. Kept checking back to see if I could do better but prices were thru the roof.

A lot also depends on the specific city/region you're planning to visit, and whether there's a major event (like a local festival) scheduled during that period. For example, you probably won't have much difficulty reserving rooms in Tōkyō for early February (even almost at the last minute), but for that same period, booking even as far ahead as 6 months in advance might not be early enough for Sapporo (due to the Yuki Matsuri).