Slice loaf into 16 equal slices, cutting to but not through bottom of loaf.
In a small bowl, combine butter, mustard and horseradish.
Spread every other slice of the bread with this mixture, beginning with first slice, so the coated slices are facing each other. Imagine cutting the loaf to make sandwiches, and that will help you figure out which sides of the bread slices to coat.
Fill the coated slices with one slice of ham, one slice of cheese and green pepper rings. Wrap well in plastic wrap and chill. To serve, cut between unfilled slices to form sandwiches.