The third question presented by Scholastic is, in my opinion anyway, a bit of a lame one. The third question is "Will Hogwarts Reopen". Whether or not the school officially reopens is, to me anyway, not the point. Whether or not the school reopens to the rest of the students doesn't seem like a big point to me. Hogwarts will still play a major role in the seventh book whether it's open to the general student body or not. Harry will, without doubt, return to the school. He has to. Symbolically, there is too much invested in the school for it to disappear from the charts now.
In an attempt to make this question more well researched than it is, I went to Quick Quotes via Leaky to look up any quotes from Jo on Hogwarts that might prove important. Most of the quotes have been more related to the inhabitants of the school (including the sorting hat and Peeves) and a bunch of random statistics of Hogwarts student numbers etc. Most of the quotes aren't related to the importance of the school itself as a building/symbol. The symbol of the school is undeniable-and the symbol of the houses themselves. Jo compared them to the different elements of the earth (water, fire, earth, wind for Slytherin, Gryffindor, Hufflepuff and Ravenclaw respectively). She's talked about how "Ravenclaw will have its day". She's talked about how students in each of the houses that she has named also have parentage mapped out so that she knows who has death eater parents/pure blood parents/muggle parents/etc. and that it will be important later on. She's mentioned several things in relation to the founders and the houses that seem to lead to Hogwarts remaining open, or at least important in the next book.
So in conclusion-I'll say that Hogwarts WILL reopen, on the basis of needing some convenient way to rally students and the youth in general (since Dumbledore has said many times that there is a kind of power in being young that the old ignore). Maybe a DA rehash? Hmm...But yes. Hogwarts will reopen.