Walnuts contain fewer carbs than almonds, peanuts, pistachios, and cashews. Plus, they have more antioxidant power than any other nut. Fourteen walnut halves (about 1 ounce) contains only 4 grams of carbohydrates, half of that coming from fiber. One ounce of walnuts also contains 10 percent of your daily intake of magnesium and 2 1/2 grams of healthy omega-3 fats. Walnuts are a great low-carb snack that can be proportioned ahead of time and left in your desk drawer for when you get hungry.