My kids can have snacks whenever they like but generally ask mostly because of their age.
I tend to find snacks are an important part of our diet. I just choose them really carefully. I have two skinny kids who appear to survive on fresh air at times. Whilst the eldest is now getting into her meals and will eat 80-90 % of most main meals its is only a recent thing. Prior to that my eldest had no apetite and looked so skinny she is now on the slim side of average. My 2 yr old eats very little.
If we have snacks little and often they are are happier and generally more willing to sit down to a meal. We basically don't have any sugary treats on a day to day basis but have things like nuts, no salt crisps, vegetable crisps, veg, cheese, home made yogurt, bread and butter, fruit like apples and bananas, rice or corn cakes and hummus/soft cheese.
We do have days when we have cake or chocolate or ice cream or something, but its not the mainstay of our diet and we don't often have pudding. I don't ever buy soda for having at home I might have it out of the house but the kids never do. I only buy fruit juice for birthdays. Its nice to have those treats but not at the core of your diet especially not for kids with small appetites.
My son has a problem with his enamel, its not formed properly, so we avoid things like fruit juice, dried fruit, sugar etc.. Its made realise how harmful sugar and acidic food can be and how skewed a lot of the ideas I had about healthy snack food was when my daughter was tiny. Everyone I knew used to give their toddlers dried fruit and fruit juices as a staple and a lot of childrens food here is sweetened with apple juice.
It can be expensive, nuts are really pricey at the moment. But then so are pre packaged snacks. I usually go shopping once a week but would top up if I have forgotten something critical.