The cream cheese and horseradish spread acts as the glue in this piled-high sandwich.
In a small bowl combine cream cheese and horseradish. In a large bowl combine 1 tablespoon of the olive oil and the red wine vinegar. Add arugula and apple slices and toss to coat. Spread cream cheese mixture one side of each bread slice. Top four of the spread slices with ham, chicken, and apple and arugula mixture; add remaining bread slices, spread side down. Brush outside of bread slices with remaining 1 tablespoon olive oil.
Place sandwiches (half at a time, if necessary) in a very large skillet or griddle; Cook about 6 minutes over medium heat or until bread is toasted, turning once.