At that age we put a cookie tray into the fridge with cut carrots, cut up celery (standing up in a cup of water) yougurt, cheese slices, an orange, an apple, turkey slices, some hard boiled eggs, etc. These things were free to dd at any time, without asking. If it was on the tray, she could have it.
I am very sensitive to saying "no" when dd asks for food. TBH I don't even like to be asked, it makes me feel uncomfortable to be "asked" to eat.
So.....the tray was hers, any time (although I'd remind her if I was, say, cooking dinner, "Choose something small ok? Dinner is in 20 minutes." ) No asking permission....you just listen to your body.
I think it's great when you can give kids control in that way. The bonus is that you'll find out if she is in fact "hungry" or does she just want sweets. If she is truly hungry than what's on the tray will work out for her.
She may overindulge with the tray at first because of the novelty, but that will stop. I highly recommend removing yourself from any struggles over food, as much as humanly possible. My dd eats like a lumberjack....I remember posting about how much she eats, and how fast she looks for more! The tray is hers, and I really love leaving it to her.