When Poppy says shes hungry I say to her get something from the snack drawer or fruit bowl. She quite happily helps herself and it also gives them independence with having some of their own responsibilities.
We can have anything from croissants, cereal bars, raisins, breadsticks, veggies crips, fruit from the fruit bowl, or even fridge items like cheese, yogurts, or smoothies. We are very aware of certain sugary items in kids snacks so we limit the amount the kids can have. At one point we completely stopped all sweets and chocolate and anything above 5g sugar in food. This was extreme and wasn't sustainable especially during birthday parties and family gatherings etc. So we gradually brought it back into her meals and snacks.