The referring site will get the entire URL of the iframe, and you can't embed an iframe by POST. So you could maybe pass the variable on with JavaScript:
(parent page)
<script>
var not_visible_to_referrers = 'data';
</script>
<iframe src="iframe.html?other=variables&to=pass"></iframe>
(iframe html)
<script>
var hidden_thing = top.not_visible_to_referrers;
</script>
Though at that point, you may be just as well-off putting it in the user's session and having the iframe retrieve it.
Alternately, you could make a link-shortening service of your own. Create a database table with the columns 'short_url' and 'full_url'. Instead of linking to the other site's full url, put it in the table with a random short_url, and link to /refer.php?short_url=4123. refer.php would look up the full URL and do a 301.