Bring a medium saucepan of water to a boil. Add corn and cook until just tender if using fresh (about 2 minutes), or until heated through if using frozen (about 1 minute). Drain.
Whisk together oil, vinegar, cumin, salt, and pepper in a large bowl. Squeeze excess liquid from cucumber, apples, and carrots with your hands and discard. Add vegetables, apples, and parsley to the bowl with dressing. Toss until well combined. Serve at room temperature or chilled.