My Riding Stables 2: A New Adventure (UP)

There are outfit pieces that you can buy from the online shop on the computer (all in all, they'll cost about $4700).  Unless I hit a beneficial glitch, you don't need to buy any of them.  Instead, you need to collect eight outfit pieces that are hidden in treasure chests scattered around the map. You need to ride up to a chest, dismount then open the chest to add the item to your inventory. 
 
--  You should see this while doing the Through the Forest training, up on a small hill, around the fifth checkpoint marker.  Just circle back for it once you've finished the training or start the training again and quit out when you reach it (stylish top hat).
-- Cross the bridge, turn left, then ride to the lake.  You'll see this right where the river meets the lake (legendary western boots)
-- Cross the bridge, turn right then follow the river until it hits the lake. Continue following the lake (keeping it to your right) until it turns right and in front of you is a path up into the mountains.  When facing the mountain path, turn left until you see a big brown patch leading behind a small mountain.  Continue turning left until you see a second small mountain - ride between those two mountains - you'll be on a huge brown path the entire time. At the end of that path is the chest (western pants)
-- Cross the bridge and follow the brown path until you hit the sand.  Once on the sand, ride forward until you hit the water. Turn left and follow the rocks until you hit another big section of water.  At that new section of water, turn left and follow the rocks.  At the point where the rocks turn and you're riding away from the water, look at the rocks and you'll find a small alcove with the treasure chest tucked inside (legendary western hat)
-- Start the third training (Ride across the Plain), ride through the first marker, get to the second and quit the training.  Take the right fork (the left one would have led to the next training marker), then at the next fork, go left.  At the top of the hill you'll find the chest (elite riding jacket)
-- Start the third training (Ride across the Plain) and immediately quit it. Turn right and ride to the cliff.  Keep the cliff on your left and as soon as it turns left, take a sharp left to start going up a grassy slope.  The slope will split into three paths - the chest is at the end of the middle path.  You should also see this chest in the middle of the seventh training (Hairpin Challenge); you can grab it then as well (western top).
-- Start the fourth training (To the Beach). Go through four checkpoints, then stop at the fifth. Immediately to the right of where the fifth checkpoint was is a hidden path behind the large rock, then the chest is right there (elite jodhpurs)
-- Finish the ninth training (At the Top). Turn around and follow the path until it forks, then turn right.  Follow the path as it goes up and downhill to another fork and turn right (the fork will be going behind you). You should see the chest as soon as you turn around (elite riding boots).
 
There's also seven chests that give money:
 
-- Finish the second training (Between Sandy Dunes), then keep the water on your left and ride until you find it, right where the sand runs into the gray cliffs ($1,000).
-- Fo to the bridge but don't cross it.  Instead, turn right and follow the brown path and you should see this just before a sharp right turn in the path, by a large tree. In the river behind it is a large flat rock.  If you see jumping hurdles, you've passed it ($50).
-- Cross the bridge, turn right, then get off the horse as soon as the river turns.  You'll find the chest behind a bunch of rocks ($100)
-- Cross the bridge and follow the brown path (forward at the fork) until you hit the sand.  Once on the sand, ride forward until you hit the water. Turn left and follow the rocks until you hit another big section of water.  The treasure chest will be among some rocks on your right ($600).
-- Leave the stables via the brown path going out from the right of the house.  Take the path right and ride left around to the head of the lake.  Once you're at the head of the lake, you'll be in a hilly area.  On the ground you should see several paths forming an X; on top of the hill just past that you should see the chest ($200).
-- Exit the stables area via the brown path to the right of the house. Follow the right path at the fork, then left at the next fork.  Follow this path into the mountains. Take the left fork and ride through the mountains until you hit another fork - take the left one, which will go down past some really large boulders. As soon as you go through a really narrow opening on this path, slow down. Pass two large boulders on your right, then look left to find the treasure chest ($1,500)
-- Start the ninth training (At the Top). You will see this chest on your left between the seventh and eighth checkpoints, among some trees ($400)
 
The developers actually sent me an overhead map with all of the chest locations marked, if my directions don't help.  You'll still need to do a little thinking, as there's no in-game map to compare it to.
 

 
None of the outfit parts are helpful in the game, because they're entirely cosmetic.