disclaimer: i have never worked at anything like this.
Is your goal to be an executive there? If yes, then almost all of them will have college degrees, period. Managing parks with $100m's in revenues typically require diverse skills incorporating finance / business / legal. HR is also likely to be VERY important as they employ so many people and so many seasonal people.
One idea would be to go to a college / university very close to a major park, and try to combine internships and co-op type programs alongside your 4 year degree. That would typically get you a huge leg up in terms of experience - and might help pay the costs of college as well.
Lastly, I'm not sure going to an expensive or super-selective college would make that much of a difference.