At least in James Bay communities, I know that babies are given Tri-Vi-Sol, which is a vitamin supplement, and mothers are given Materna. Not all individuals take those supplements or give them to their children. But I think it's really important to remain food-focused and not nutrient-focused, because individuals eat food, not nutrients.
In the United States, there has been the horrible thought of adding vitamins and minerals to pop because that's what children are drinking, which is a hideous notion. SunnyD markets itself that way. It's sugar water, with a few vitamins thrown in. It's mostly sugar.
I can't see that the increasing prevalence of obesity over the last few decades has to do with rampant vitamin and mineral deficiencies in children. I don't think the diet has changed enough to allow for that hypothesis. So I don't know any research specifically that has looked at whether supplementing children would reduce rates of obesity. I doubt it. And again, I think it's very important not to move away from food, because individuals eat food, not nutrients.