The Fire Arrows are obtainable after beating the Water Temple. To get the Fire Arrows, go to Lake Hylia as Adult Link and fire an arrow at the sun right when it rises. Keep in mind you have to fire at it as it starts to peek up, not when it's high up in the sky. The arrow will freeze in the air and drop to a little piece of land out in the lake. If you go pick up the arrow, it is on fire, and you obtain the fire arrows.
The Ice Arrows are located at the Gerudo Training Ground, and can also be obtained after the completion of the Water Temple. Go to the Gerudo's Fortress as Adult Link and rescue the four carpenters from their prison cells and you will encounter a Gerudo. She says that she was put in charge while Nabooru is at the Spirit Temple. She will grant you membership to the Gerudos. After this, you can talk to the Gerudo outside of the door with the gate blocking it. If you pay her, she will grant you access inside. This is like an optional mini-dungeon. There are switches and puzzles and the like inside. Going through the various trials on the door on the right or left will grant you small keys, which you will use to unlock various doors inside of a maze-like part of the dungeon that is located in the door straight ahead from the entrance. After you obtain all the small keys there will be a switch in the middle of the room(I believe it is inside of a breakable crate) that will make the chest appear in one of the rooms. Go find that room and open the chest to obtain the Ice Arrows. Keep in mind that the tasks inside of the Gerudo Training Ground are not easy, especially if you're doing Master's Quest.
The thing about the Ice Arrows is that you go through so much do get them, but really they have almost no use. The only thing they can be used for is shooting enemies. They don't have a real purpose for any other part of the game.
The Light Arrows are unavoidable as part of the story.