Is it possible to hide page numbers from arbitrary pages? Like say, the 3rd, 7th and 50th pages? The real catch is that the entire document must be contained in a single div.

What I'm really looking for is something like @page:third { @top { content: none; }}

Is this possible, or an I dreaming?

This is not really possible unless you explicitly create the pages yourself, like this:

<div class="page">Page 1</div>
<div class="page">Page 2</div>
<div class="page no-header">Page 3</div>
<div class="page">Page 4</div>

In this case the pages have explicit markup and you can control exactly which pages will have headers/footers. However, if you flow all the content into a single large div (like a chapter, say) it is not possible to select arbitrary pages of the output and suppress headers/footers on those pages.