Put 4 cups cold water in a medium saucepan and bring to a boil over high heat. Add the tea bags, remove from the heat and let steep 5 minutes. Add in the sugar while it is still warm so that it will dissolve. Refrigerate until cold, at least 30 minutes.
Put the cold tea, berries, yogurt and a few cups of ice in a blender and blend until smooth. Divide the drink among 4 tall glasses.