I have just been struggling to track down why the cookie for one of my sites was not always being set in IE10 (also tried it in IE9 compatability mode).
It eventually transpired that my code was sending the cookie twice:
EXPIRES 20/06/2013 23:59:59
Firefox ignores the first instance and uses the second value (as this appears slightly later in the http header).
However, IE would sometimes do this, but more often it would simply ignore the cookie information altogether.
The small privacy symbol did not appear either to indicate that the cookie was being ignored.