I'm a grazer... though I always bring containers of chopped up fruit and stuff to snack on during the day at work. And things like carrot sticks, radishes, cucumber, etc. I also have my Hex things like Alpen Light bars and Babybel Light cheeses... but I couldn't live without snacking. And I still lose weight. I think the trick is to try and snack on super-free foods if poss.
Though theoretically you can eat any of the free foods you want, logic would suggest that eating the lower calorie ones will yield a better weight loss.