This sounds like a ton of clean up! You absolutely have to pick up all the balloon pieces due to the litter problem and the risk to birds/wildlife, and the ice cream sounds like a lot more fun for the kid on top than the kid on the ground. I'm not sure how you keep the ice cream frozen in Arizona - no on in our neck of the woods plays this game so I'm sure it's more challenging in your climate. And then everyone is sticky and unable to go home in the car without messing up the seats. Do you have a way to hose them all off and put them in a change of clothes, plus hose down the spilled ice cream so as to not make the park a mess for the next visitors? And if you insist on this, do make sure that none of the kids has a sensitivity to insect bites, as the ice cream mess will attract a variety of undesirable bugs. And are you doing something for eye protection? I'd be sure to tell the parents a lot more than "they'll get wet."
You know what kids really love (especially because many of them haven't played them)? Old fashioned party games! Our neighbors have been doing this for some years, and the kids are raving about them! They are so tired of bounce houses and they just love the 3-legged races, the sack races (get old pillow cases from neighbors willing to donate, or go to the discount store), the potato/wooden spoon races, and so on. These are not just "exercise", they are also about balance and patience, not just speed - so it's good for not-so-athletic kids (the aggressive kids usually fall down or drop their potatoes!). Supplies are cheap (a 5 pound bag of potatoes and some wooden spoons from the dollar store, for example).
You can google these games, but I also went to the library to get a book so I could see all the suggestions and review the "rules" (You might have to look for camp games vs. party games - you'll get good ideas there as well).
ETA: Just checked the link posted by Isn'tThisFun. So many of those ideas look wonderful!!