I modified your code a little. Try this:
var active = $.cookie('active'),
$h3 = $("#menu h3"),
$activeH3 = $h3.filter('#' + active);
$h3.click(function(e, speed) {
$("#menu ul ul").slideUp(speed);
if (!$(this).next().is(":visible")) {
$(this).next().slideDown(speed);
$.cookie('active', this.id);
}
});
if ($activeH3.next().is(':hidden')) {
$activeH3.trigger('click', [0]);
}
Make sure you also set ids for your h3
elements.