The Forgotten Sword
You must first have completed the sidequest "The Eighth Heroine" before you can talk to Bozai for this sidequest. Learn about it here. Once it's done, Bozai will retire under a tent. Again, dressed in the female Gerudo armor, talk to him for another favor.
Tell him you want his Snow Boots and he will tell you that in urban legend, The Eighth Heroine had a sword. But when we saw the statue, there was no sword. Bozai wagers the sword couldn't be too far and is still in Gerudo Highlands.
The sword's precise location is actually on the southeastern corner of Gerudo Summit. Travel there again and take a photo of the sword which is stuck in the ground. Bozai was right. It's a hefty sword (given how big the statue was, is this a surprise?) so you can't miss it. Just beware the Silver Moblin sitting by it.
Return to Gerudo Town and show the photo to Bozai. Then ask him for his Snow Boots and he will give them to you. Too bad for poor Bozai...he doesn't seem to realize who he is asking out on a date.