I have done some testing on this and can confirm that HTML Editor values do not get set properly when coming from a cookie. I have logged a bug for this but I was not able to find a way to get the cookies to work with the HTML Editor instance.
As a workaround I was able to store the HTML Editor value in a session variable, then I set the initial value of the editor to this session variable. This seemed to work out ok.
On the page that the form is posting to you would add in a piece of code to the top of the page like this:
<?php if(!session_id()) session_start();
$_SESSION['test_val'] = $_POST['test'];
Then in your HTML Editor instance use this as the initial value code:
<?php echo ((isset($_SESSION["test_val"]))?$_SESSION["test_val"]:""); ?>
You will need to update the word 'test' in these code examples with the name of your editor. If you have any problem with this let us know and post back with the pages in question and we can show you how to add this.