Preheat the oven to 200℉. Thoroughly rinse the cranberries and pat them dry with a towel. Pick out any squashy or bad berries. Set aside. In a medium sized mixing bowl, whisk the egg whites on high with an electric mixer for about 1 minute until foamy. Pour in the cranberries and mix to coat all the berries in the egg whites.
Pour 2 1/2 cups of powdered sugar into a gallon ziploc bag. Carefully transfer half of the cranberries into the powdered sugar using a slotted spoon or strainer. As much as possible, avoid excess egg whites going into the bag with the cranberries. Too much liquid makes it soggy. Gently shake that bag side to side until the cranberries are thoroughly coated in sugar. Ideally, they should be all white. If you have lots of cranberries that don't look fully coated, add another cup of sugar. The cranberries need to be fully coated before baking.
Pour the whole bag onto the cookie sheet pan and spread the berries out into a single layer by gently shaking the pan. Try not to have the berries touching each other if possible. For the remaining half of the cranberries, add another 2 1/2 cups of sugar to the bag. Spoon in the rest of the cranberries, shake, and spread onto the pan. If your cookie sheet is small, you might need to use two cookie sheets.
Place the cranberries on the middle rack and bake for about 15-20 minutes. Keep the oven door closed, turn off the oven, and let the candies cool down for 45 minutes-1 hour.
Use a slotted spoon or strainer to gently spoon the candied cranberry snowballs into a serving dish. Store in the refrigerator until ready to enjoy!