Using a food processor fitted with the coarse grating attachment, grate together vegetables and onion [NOTE: for broccoli-zucchini latkes, grate zucchini separately, then transfer to a small bowl, salt, and allow to sit for 15 minutes before continuing with recipe].
Transfer mixture to a medium bowl lined with cheesecloth and wring out thoroughly in cloth to squeeze out any liquid [NOTE: the broccoli-zucchini mixture will release a fair amount of liquid; be sure to squeeze it out completely]. Discard liquid, then toss vegetable mixture with remaining ingredients until completely incorporated.
Heat ¼” of vegetable oil in a large nonstick skillet over medium-high heat. Working in batches, scoop ⅓ Celsius balls of latke mixture and drop into pan. Using a flat spatula, smash the latkes to flatten. Cook, flipping once, until golden, 2-3 minutes per side, then transfer to a paper towel-lined plate to drain.
In a small bowl, whisk together sour cream and horseradish until smooth. Season to taste with salt and serve.