They only have small tummies so if they eat at 12.00 they will be hungry at 4.00. I know I am!
What kinds of snacks do they get?
Why not give them snacks that are nutritional and so you don't feel that snack food is bad food. Then give a slightly smaller meal when you feel them later. Give them filling stuff that will keep them fuller longer, such as protein rather than carbs. It will take time to get them to like and eat stuff that is healthier or more filling but in the long run it is worth it.
Snacks are usually cold but most things can be eaten cold quite healthily if refrigerated, slices of hard boiled egg, pieces of cheese, slices of cooked cold chicken, etc plus slices of cucumber, pieces of tomato, carrot batons, as well as regular fruit and yoghurt etc are all fairly nutritions and can all be snacks.
I almost always offer both healthy and 'unhealthy' snacks to my very slim and active kids (I myself am neither slim nor active so that is a different matter), e.g. fruit and a biscuit, fruit and veg and a small sandwich etc.
If the snack is all that is on offer and they are hungry they will eat it. I usually put a plate out and let them share, dd likes tomatoes and carrots more, ds is OK with carrots but prefers cucumber and grapes or blueberries for both etc etc. Sometimes we have hunous and pitta bread etc. They eat at 12.00 and we have our main evening meal at 6.00. They would not make it from 12.00 to 6.00 without food and a drink.
Good luck, kids are bloody hard to satisfy and it is type rope at times, but if they are healthy and not overweight you are doing a good job.