Do what Google is doing. Yes, Google is doing this same trick to login the user to YouTube and other Google services which are on different domains.
Create a PHP file that sets the cookie on all 3 domains. Then on the domain where the theme is going to set, create a HTML file that would load the PHP file that sets cookie on the other 2 domains. Example:
<html>
<head></head>
<body>
<p>Please wait.....</p>
<img src="http://domain2.com/setcookie.php?theme=whateveryourthemehere" />
<img src="http://domain3.com/setcookie.php?theme=whateveryourthemehere" />
</body>
</html>
Then add an onload callback on body tag. The document will only load when the images completely load that is when cookies are set on the other 2 domains. Onload Callback :
<head>
<script>
function loadComplete(){
window.location="http://domain1.com";//URL of domain1
}
</script>
</head>
<body onload="loadComplete()">
setcookie.php
We set the cookies on the other domains using a PHP file like this :
<?php
if(isset($_GET['theme'])){
setcookie("theme", $_GET['theme'], time()+3600);
}
?>
Now cookies are set on the three domains.
Source - My Blog