That area would be monitored by DNR (Department of Natural Resources) personnel. Most of them drive trucks or perhaps an SUV around here. I'm sure there would be someone in Bremer County whose job entails cleaning and monitoring a park like this. My guess is that it would not be a daily or even weekly job, but maybe. There are many other recreation spots in the area DNR do take care of - from collecting money at designated campgrounds to clearing out broken branches in the parks, mowing, etc.
Again, I have never been there, but from aerial pictures and from growing up in Bremer County, you would have to walk a significant distance from the road to the bodies. The Cedar Rapids Gazette has a large amount of great aerial pictures on their website - the link was somewhere up thread - and those can show you the distance from the turn-around to the locations of the bodies.
I have never heard of the parks hiring students, but the DNR might have interns. I've never heard of this though.