Swedish vinegar: Place all ingredients in a saucepan. Bring to a boil over medium heat, stirring until sugar dissolves. Remove from heat, and let cool.
Beets: Put beets in a medium pot; add bay leaves, allspice berries, horseradish, and water. Bring to a boil, and cook until beets are tender when pierced, 45 minutes to 1 hour. Drain. When cool enough to handle but still warm, peel and cut into quarters.
Transfer beets to a nonreactive container with a tight-fitting lid, and pour vinegar over them. Cover, and refrigerate at least 2 days and up to 1 week before serving.