Cook pasta, uncovered, in 1 to 1 1/2 quarts boiling water until barely tender to bite, 6 to 7 minutes. Put shelled peas in colander. Pour hot pasta and its cooking water over peas; drain. Let pasta and peas stand a few minutes, then rinse with cold water; drain well.
Mix mayonnaise, onion, horseradish, and garlic. Stir in peas and pasta. Add salt and pepper to taste. Place lettuce leaves on serving dishes. Spoon salad onto lettuce.