There are a total of twenty feathers scattered around the map of A Short Hike. Though finding them is easy at first, finding the last few can be a bit of a struggle. Below I list all gold and silver feather locations.
Note: All cardinal directions are given based off the map and the in-game compass which can be obtained by the wolf on the south end of the map.
Map of Locations
Goat ranger at Visitor Center
The goat ranger at the Visitor Center sells two gold feathers for 40 coins each.
Mound Northwest of Visitor Center
There's a mound northwest of the visitor center. To get up there easily you need one feather but there are ways to reach it with no feathers.
In practically the middle of the western portion of the map, near Royal Ridge, is a stone tower. On top of the tower is a chest holding a golden feather.
On the northwestern-most part of the island there is a court where you can play a young bird in a game of beachstickball. Although the game has multiple rewards, the first, awarded after you and your partner hit the ball 10 times, is a gold feather.
Ledge above Graveyard
By far one of the more difficult feathers to find unless you've soared around the island a few times. On a cliff above the graveyard is a chest and in that chest is a feather. The graveyard is on the northwestern-most part of the island near the Beachstickball court. To find where to climb the wall, look for Avery or the tree with the ribbon tied around it. The chest is directly up from there.
Cliff North of Meteor Lake
North of the lake, way up on the cliff side is a small outcrop where you can find a feather freely floating. There's a flower on the way there to make things a bit easier.
In Her Shadow
In Her Shadow is the only treasure map quest that results in a golden feather (though the others give a bunch of money). You don't need the treasure map, but if you want it it can be found at the boat on the east side of the island.
If you have the shovel and don't care for riddle solving, the chest can be dug up north of the lighthouse at the end of its shadow.
On Top of Lighthouse
On top of the lighthouse there's a balcony with a chest on it. Inside is a feather.
Hidden in Forest
There's a dense forest southwest of the lighthouse. Within you will find a gold feather on top of a rock.
Cliff below Outlook Point
On a cliff west-southwest of Outlook Point nestled on an outcrop above the trail.
At Outlook Point, near the scenic platform is a chest with a gold feather.
There's a large cliff face preventing the player from ascending higher up the mountain (at least without feathers or the bucket). At it's base it a tough bird reselling four gold feathers bought from the Visitor Center for 100 coins each. Right by them is a gold feather sitting on top of a rock.
Walking around the south beach of the map you can meet a young bird who demands you get her 15 seashells.
Scattered around the island are pink, sparkly objects which are the shells needed for the quest. They are mostly found on beaches, sandy areas, or near rivers. When you return the shells to the bird she makes a shell necklace and tasks you to give it to Ranger May who is outside of the cabin you start in.
As a sort of reward (though it's framed as a coincidence), May gives you a gold feather.
Frog Building Sand Castles
At a small bay on the south side of the island is a frog building sand castles. He's the one who gives you a shovel in exchange for a toy shovel. There are numerous toy shovels scattered over the island. Once you exchange the toy shovel for a real shovel, the frog will start building more sandcastles. In order for "time to pass" allowing him to build more, you have to leave the area and come back.
The wandering artist is a raccoon that can be first encountered in the southwestern-most portion of the map. When you speak with him, he finishes by saying he'll move somewhere else to paint though it can be a bit cryptic. After speaking to him at each location, he'll eventually give you a golden feather.
Location #1 (Southwestern Peninsula)
Down to the southwestern-most portion of the island is the first place you find the artist. You'll know you're around the right area if you see a brown dog running around. Speaking to him and leaving the area will move him to the next location.
Location #2 (Lighthouse)
The Lighthouse is pretty hard to miss and the artist is just west of it. If you're having trouble, the lighthouse is also directly above Aunt May's cabin.
Location #3 (River's Source)
One of the more obscure locations, but there are only a few rivers so shouldn't be too hard to locate it. If you know where the tough bird that is selling feathers and complaining about tuition is, walking off to the left of him will lead you to the raccoon.
Location #4 (Graveyard)
On a non-descript clidd overlooking the graveyard. If it's raining you're in the right area.
Location #5 (Outlook Point)
Outlook Point is just below where the climb up the mountain gets cold enough to freeze your feathers. The artist will be right by the lookout telescope.
Location #6 (Visitor's Center)
There is a silver feather located on a mystery island just off the main island. To find it, you talk to the crocodile walking around Sid's Beach on the south end of the map.
They point you toward Outlook Point where you can peer through a set of binoculars. Moving the view to the right, you can see an island off in the haze.
The island also has a tall peak and once you go there and climb to the very top, you'll find a silver feather.
A Goat's Watch and Tough Bird's Tuition
The quest can be a bit sneaky if you don't pay attention to dialog. In the center portion of the southern part of the map is a camper site where you can meet a goat. The goat tells you their painful story of how their watch has gone missing and they hope someone "doesn't sell it on the Internet."
If you talk to the tough bird selling feathers, you'll find that he's selling them to pay off his tuition which, even after you buy his feathers, will cost 400 coins.
There's many ways to earn coins around the mountain. You can dig up treasure, find chests, or sell fish. Once you get enough coins you can return to him and give him the money to pay off his tuition.
As a reward, he gives you a watch eh was going to sell on the Internet.
Watch in hand, you can return to the goat who gives you a silver feather in exchange.