This page explains how to start and complete the The Forgotten Sword side quest.
How to Start the Quest
First, you need to complete the side quest The Eighth Heroine. Then go back and talk to Bozai again to start this quest.
How to Complete the Quest
First, it is recommended to follow the steps to unlock Kema Kosassa Shrine if you have not already done so. From there, you can go east to a slope that leads up to Gerudo Summit. Beware of rolling snowballs as you approach. There is a Lynel on top of the mountain, so if you don't want to fight it, go southeast. The sword is to the east of the rock formation south of where the Lynel patrols. Take a picture of it, making sure that the picture has the red exclamation mark symbol. Then go back to Gerudo Town and show Bozai the picture. He will give you the Snow Boots.