I activated this summit a few years ago, so doing this write up based on the best of memory.
Back then you did not need a permit for day hiking or staying overnight in the Three Sisters Wilderness. Today you will need to apply for an overnight permit if you are camping, as well as a day hike permit for certain trail heads. See the following link https://www.recreation.gov/permits/4675311 for info on how to obtain a Central Cascades Wilderness permit, as well as this map
