One of the Mirror of Twilight's shards is said to be on a snowy mountain, so you investigate Snowpeak.
Go to Snowpeak
Talk to Telma in Telma's Bar in Castle Town, then check the map on the table to get Snowpeak marked on your map.
Then go to Zora's Domain. After going down the waterfall from the throne room, check your map and go through the tunnel near the mark on your map, where a couple of Zora guards are standing near a small waterfall.
At the other end of the tunnel, talk to the person standing there. Ashei gives you a sketch of the creature seen on Snowpeak and in Zora's Domain. If you show this sketch to the Zoras in Zora's Domain, they will say that the fish is a Reekfish, and they will say that Prince Ralis knows how to catch that type of fish.
Meet Prince Ralis
Go to the Kakariko Graveyard and crawl through the tunnel in the back to find Prince Ralis. Show him the sketch and he will give you the Coral Earring and tell you that you can catch the Reekfish at the Mother-and-Child Rocks in the waterfall basin. The Coral Earring is automatically added to your fishing rod.
Catch a Reekfish
Warp to Zora's Domain and go down the waterfall, then swim to a ledge near the rock formation where you can see red fish. Equip the fishing rod and use it to catch a Reekfish. Then transform into a wolf and learn the Reekfish Scent.
Follow the Reekfish Scent
Go back through the tunnel from Zora's Domain to Snowpeak, and transform into a wolf to follow the Reekfish Scent. Beware of Ice Wolfos that attack; if you stray too far from the scent, you'll get lost and start at the beginning of the area. Also, if you fall into the water, you'll freeze and start at the beginning of the area.
Eventually the scent will go up a wall, so you will need to climb up some ledges. Continue following the scent and you will find a wall that you can't climb, but it has a large pile of snow on top of part of the wall. Dash into that part of the wall to make the snow come down, creating a ramp.
Continue following the scent. Look for a Howling Stone on the way. You might want to turn off your senses to make it easier to see the Howling Stone. Don't warp to the Golden Wolf yet. You will soon create a warp point here on the mountain.
Follow the scent and dig in the wall where the scent disappears. In the cave, transform back into a human. Climb the ladder and make your way past Ice Keese and vines until you reach the exit door. Go out through that door.
Continue along the path and some Shadow Beasts appear. Defeat them as you have done before. This creates a warp point.
Talk to Yeto
Up ahead, you will find a yeti named Yeto. When he asks if you're on a spiritual journey, say no. He says that he has the mirror shard at his house and tells you to slide there like he does.
Slide After Yeto
After Yeto slides away, dash into the tree, then jump onto the ice shard that fell. The path downward is straightforward, so just avoid obstacles and try not to slide off of any cliff. You can jump while sliding downward, allowing you to collect rupees on ledges and treetops. When you reach the house, the ice shard will break on the bricks. Go through the door to enter Snowpeak Ruins.