Cook eggs in a saucepan of boiling water to your liking (6 minutes for soft-boiled). Drain, refresh, peel and halve.
For horseradish dressing, whisk ingredients in a bowl and season to taste.
Combine carrot, beetroot and herbs in a bowl, drizzle with half the dressing, season to taste and toss to combine. Divide salad among plates, top with egg halves and trout, drizzle with remaining dressing and serve.