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So you are saying that a stadium such as the Cotton Bowl, an open air stadium, would not be 'premises' if it was owned by a school district? By any definition I do believe it would be construed to be a building of some sort.

In this part of Texas a number of college campuses have expansive open surroundings, and frequently these are laid out for soccer fields. No formal structure beyond a few portable metal bleachers if you are lucky. Since there is no structure, there is no building and concealed carry is a non issue. If a school district constructs a stadium at great expense and fence it in so that access is normally permitted through a specific location, what you now have here is a school facility that is off limits to concealed carry. Seems pretty simple and straightforward. You don't have to have a roof over it.

Wooow. Any good prosecutor worth his salt is going to argue that a school owned stadium, even if it open air, is a school facility, and once you enter the ticket gate, you are inside a school facility, just as you would be if entering the adjoining high school. I would encourage you to rethink the idea of taking your concealed weapon into the stadium if it is owned by the school. Recreational soccer games, played on open fields with no permanent infrastructure are another matter.