Bring 2 quarts of water to a boil in a large pot. Add carrots and snap peas and cook for 3 minutes. Remove with a slotted spoon. Add pasta to the boiling water and cook according to package directions.
Over medium-high heat in a large skillet, heat oil. Add garlic and sauté for 1 minute. Add carrots, snap peas, salt and pepper and cook for 2 minutes. Add shrimp and wine and cook until wine has evaporated. Add cream and lemon juice, reduce heat and simmer for 3 minutes.
In a large bowl, toss together hot pasta with shrimp and vegetable mixture, arugula and Parmesan cheese. Serve immediately.