Triple rinse the uncooked red quinoa. Place the quinoa in a saucepot filled with 2 cups of water. Bring to a simmer. Simmer until the quinoa gets slightly translucent around the sides, about 12 minutes. Strain the water from the quinoa using a mesh strainer. Place cooked quinoa in a mixing bowl and let cool to room temperature.
Place the mint, white wine vinegar and smoked paprika in a small bowl. Whisk to combine. Using the whisk, slowly drizzle in the olive oil to combine. Toss quinoa with ½ of the vinaigrette.
Add the squash, roasted beets, green onions and cherry tomatoes to the quinoa. Divide the mixed greens on four plates Drizzle the remaining vinaigrette over the greens. Top the greens with the quinoa mixture. Garnish each salad with some of the crumbled feta cheese.