Preheat the oven to 400 degrees F. Melt 3 tablespoons butter in a pot over medium-high heat. Add the cabbage, raisins, vinegar, cider, 1/4 teaspoon allspice and 1/2 teaspoon each salt and pepper; bring to a boil. Reduce the heat and simmer, covered, 20 minutes. Uncover and simmer until the liquid is almost gone. Add salt and more vinegar to taste.
Meanwhile, sprinkle the pork with the remaining 1/4 teaspoon allspice, 1 1/4 teaspoons salt and 1/2 teaspoon pepper. Heat the olive oil in an ovenproof skillet over medium-high heat. Brown the pork on all sides, then transfer to a roasting pan (reserve the skillet) and roast until a thermometer inserted into the meat registers 145 degrees F to 150 degrees F, 10 to 15 minutes. Transfer to a cutting board.
Boil the broth in the skillet until reduced by one-third. Mix the flour and the remaining 1 tablespoon butter, whisk into the broth and boil 1 minute. Stir in the horseradish. Slice the pork; serve with the cabbage and sauce.