Well, I don't think this will make a big differance, and really I think someone should seriously be telling Mrs. Obama off.
Right now there are two big things to consider:
#1: Kids generally don't go outside to play because they can't. Simply put our society requires two incomes at the moment, you don't have a "homemaker" parent anymore. This means there is nobody to supervise children for trips to a playground or whatever. Our society also suffers greatly for being extremely permissive and liberal in some respecs, and one of those prices we pay is society being too dangerous for children to roam neighborhoods unattended. Assuming of course local laws haven't been passed prohibiting such outright (so the neighbors won't have kids roaming their yards).
The days of yor with unlocked doors, and kids being able to frolic in the suburbs with wagons and scooters and whatever else are basically gone. Today we can't do anything about a sexual deviant until he actually molests a child and gets caught.
Welcome to the day and age of "Latchkey kids" who might come home to an empty home as young as five or six, and lock themselves in an apartment waiting for mommy and daddy to get home (providing they ever do).
The point is that none of these things are easy issues to address, but if you want to have kids playing outside more actively, you need to fix society which means you might have to make unpleasant desicians.
Ironically I think politicians like the Obamas are part of the problem as they generally support the kinds of policies that have perpetuated these problems. This of course goes well beyond the scope of this discussion.
#2: Kids don't buy their own food. You can spam them with healthy eating all you want, but the problem isn't so much kids existing off of unhealthy snack fare, typically most don't. Rather it's because your typical family goes to the grocery store and for financial reasons gets the cheapest version of whatever they are after that they can. Sure, you can talk cr@p all you want about reading ingrediants, and health information, but the bottom line is that most people can't afford to buy premium health food, and the more expensive brands. Some can, but most can't. Your typical shopper looks at the price, and maybe the weight, as their primary concern (ie the overall value).
The result is that while admittedly kids AREN'T getting as much exercise as they might otherwise be getting (and would have in earlier eras), a lot of the weight and health problems comes from the fact that while mom and dad make them eat their vegetables and things they might not want, they are also eating whatever meat was on sale that week (and was probably on sale due to being unusually fatty or whatever), whatever other products were cheapest, and their snacks are probably as often or not selected by a similar criteria.
This is called "reality".
So really, you can tell kids whatever you want. You can probably even get them to genuinely agree with you on a lot of this stuff. But in the end it doesn't matter since the problems aren't something that can really be controlled from their end. Nor is anyone going to just promote some educational propaganda and magically get parents to be home more, clean up the streets/make society less dangerous, or put more money into pockets to buy healthier, higher quality food products.