Cook the tortellini according to package instructions, adding the snap peas and tortellini to the pot at the same time. While the pasta and peas are cooking, make an ice water bath: Dissolve the salt and warm water in a large bowl. Add 4 cups each ice and water and reserve. Drain the pasta and peas, cool in the ice water bath for 2 minutes, then drain again and transfer the tortelloni to a large bowl. Add the vinaigrette, carrots, onions, and cheese and season with salt and pepper to taste.