My original notion was,
A) If there's a movement and a destination (as in the case of thumbing a book to reach a certain page), it should be to:
Class, open your books to page 13!
B) If there's none, then at:
There on the counter rested my cookbook, open at page 13.
The tome fell open right at the middle page.
Then I asked around and rummaged in corpora and found out that my reasoning was flawed. [IMO, there's either something wrong with logic or with language—or both. Somebody fix the whole mess please.] In fact, when it comes to opening or being open, the preposition is almost always to in AmE, whereas BrE is probably mixed, and (sometimes?) there is even a strong preference for at (especially in cases like B above).
I'll close with some of the search results that I mentioned, and leave the rest to others to hash out. Speakers of other dialects are more than welcome to chip in as well!
- shut the book for a moment, then open it back up to page one and begin again – COCA
- Students, if you could please open your math books to page two – COCA
- Open your grammar at page fourteen – BNC
- every time I took up the book it opened at page 92, although I have never deliberately read that page – BNC
- I happened to open the Rome Treaty at page 89 of the English text – Hansard Corpus
- his first act on sitting down to breakfast was to open the tabloid at page three, fold it and prop it against the sugar bowl – BNC