Place the shredded potatoes in a 2 quart bowl. Add the salt and ice and enough water to cover the potatoes. Stir to mix in the salt. Cover the bowl and place in the refrigerator for 2 hours. Place the soaked potatoes in a colander. Rinse with cold water then drain completely. Heat a large, cast iron skillet over medium heat. Add enough vegetable oil to lightly coat the bottom of the pan. When the skillet is hot, add the drained potatoes to the skillet and evenly spread them around (do not press them down or they will get mushy). Fry, without stirring, until crisp on the bottom, about 12-15 minutes. When browned, carefully flip them over and cook for 3-5 more minutes. Do not cover the hash browns while cooking.