Wash and pick over the cranberries. Put the cranberries in a saucepan with the water and boil over high heat for 3 to 4 minutes. The cranberries will soften and begin to pop.
Dissolve the gelatin in a 1/2 cup of water. Line a bowl with plastic wrap.
Put the boiled cranberries in the food processor or a food mill.
Add the sugar and the dissolved gelatin to the bowl and process until smooth.
Add the horseradish. Pulse it and then give it a taste. Add more horseradish if you want a spicier cranberry sauce.
Pour the cranberry sauce into the prepared bowl. Cover the top with plastic wrap and chill in the fridge overnight or for a few days.