Place goat cheese, yogurt, and sugar in a food processor; process until smooth.
Transfer to a bowl.
Place cream in a medium bowl; beat with a whisk or in a stand mixer until soft peaks form (about 2 minutes). Fold cream into goat cheese mixture. Spoon 1 tablespoon low-sugar apricot preserves into each of 4 glasses; top each with a little less than 1/4 cup goat cheese mixture and 2 gingersnaps, crushed. Repeat layering with the same amount of jam and cream; top each parfait with 1 crushed cookie.
