Prepare grill for cooking. If using a charcoal grill, open vents on bottom of grill, then light charcoal. Charcoal fire is medium-hot when you can hold your hand 5 inches above rack for 3 to 4 seconds. If using a gas grill, preheat burners on high, covered, 10 minutes, then reduce heat to moderate.
Cut kielbasa crosswise into 4 long sections, then halve each section lengthwise. If using kosher salami, cut lengthwise into 8 (1/4-inch-thick) slices. Trim off skin if desired.
Whisk together oil, mustard, horseradish, vinegar, honey, salt, and pepper in a small bowl until emulsified. Toss lettuce with half of vinaigrette and reserve remainder.
Grill tops and bottoms of rolls on lightly oiled grill rack, covered only if using a gas grill, turning over once, about 2 minutes total, then transfer, cut sides up, to a platter. Brush cut sides of top halves with remaining vinaigrette and mound salad on bottom halves.
Grill sausage on lightly oiled grill rack, covered only if using a gas grill, turning over once, 3 to 4 minutes total, then arrange on top of lettuce (2 pieces per sandwich) and cover with top halves of rolls. Cut sandwiches in half crosswise.
Sausage and rolls can be grilled in batches in a hot lightly oiled well-seasoned ridged grill pan over moderately high heat.