Bring first 3 ingredients to a boil, stirring often, in a saucepan over medium-high heat; add cranberries.
Return mixture to a boil. Reduce heat, and simmer, stirring often, 10 minutes or until cranberry skins begin to pop and mixture begins to thicken. Remove from heat.
Stir in preserves, horseradish, and mustard; remove pan from heat, and let sauce cool. Cover and chill until ready to serve.
Note: Sauce may be stored in an airtight container in the refrigerator up to two weeks.