Place the water, cranberries, and sugar into a small saucepan set over medium-high heat and simmer until the berries begin to pop, approximately 7 minutes. Remove from the heat. Puree with a stick blender, blender, or food processor for 1 minute. Pass the mixture through a fine-mesh strainer directly into a metal 13-by-9-inch pan. Do not press on the skins; simply allow the juice to drip through the strainer. Add the zest and stir to combine. Place in the freezer until set, at least 6 hours and up to overnight. Once frozen, scrape the mixture with a fork to create a shaved ice texture. Serve immediately.