Go fish: It's never too early in the morning to get in your daily dose of disease-fighting omega-3s.
Place potatoes in a large saucepan; cover with cool water. Bring to a boil over high heat. Reduce heat to medium-low and simmer until tender, 12 to 14 minutes. Using a slotted spoon, transfer potatoes to a plate lined with paper towels. Add vinegar to simmering water in saucepan. Break eggs into individual cups and slip into water, 1 at a time, as close as possible to the surface. Simmer until whites are set and yolks are still runny, 3 to 4 minutes. Using a slotted spoon, transfer eggs to a separate paper towel-lined plate.
Heat oil in a large nonstick skillet over medium-high heat. Add potatoes, salt, and pepper; cook, stirring occasionally, until very lightly browned, 3 to 4 minutes. Add spinach; cook, stirring often, until wilted, about 1 minute and 30 seconds. Stir in horseradish.
Divide hash among 4 plates. Top with trout and poached eggs. Serve with lemon wedges.