Setting Cookies Across Subdomains Or Paths

I am setting a cookie on a subdomain:
http://store1.mydomain.com

Then the store takes me to a shopping cart that is at:
http://shopping.mydomain.com

Somewhere the following code (taken and modified from The JavaScript Source)
is broken between domains, because when I click my "store" link that should
read the cookie and send me to store1.mydomain.com or storeN.mydomain.com I
get the default template store.

<SCRIPT LANGUAGE="JavaScript">
<!-- Original: Ronnie T. Moore -->
<!-- Web Site: The JavaScript Source -->

<!-- Begin
var expDays = 30;
var exp = new Date();
exp.setTime(exp.getTime() + (expDays*24*60*60*1000));

function getCookieVal (offset) {
var endstr = document.cookie.indexOf (";", offset);
if (endstr == -1)
endstr = document.cookie.length;
return unescape(document.cookie.substring(offset, endstr));
}
function GetCookie (name) {
var arg = name + "=";
var alen = arg.length;
var clen = document.cookie.length;
var i = 0;
while (i < clen) {
var j = i + alen;
if (document.cookie.substring(i, j) == arg)
return getCookieVal (j);
i = document.cookie.indexOf(" ", i) + 1;
if (i == 0) break;
}
return null;
}
function SetCookie (name, value) {
var argv = SetCookie.arguments;
var argc = SetCookie.arguments.length;
var expires = (argc > 2) ? argv[2] : null;
var path = (argc > 3) ? argv[3] : null;
var domain = (argc > 4) ? argv[4] : null;
var secure = (argc > 5) ? argv[5] : false;
document.cookie = name + "=" + escape (value) +
((expires == null) ? "" : ("; expires=" + expires.toGMTString())) +
((path == null) ? "" : ("; path=" + path)) +
((domain == null) ? "" : ("; domain=" + domain)) +
((secure == true) ? "; secure" : "");
}
function DeleteCookie (name) {
var exp = new Date();
exp.setTime (exp.getTime() - 1);
var cval = GetCookie (name);
document.cookie = name + "=" + cval + "; expires=" + exp.toGMTString();
}

var favorite = GetCookie('store');

if (favorite != null) {
switch (favorite) {
case 'store1' : url = 'http://store1.mydomain.com/'
break;
case 'store2' : url = 'http://store2.mydomain.com/'
break;
case 'store3' : url ='http://store3.mydomain.com/'
break;
case 'storeN' : url = 'http://storeN.mydomain.com/'
break;
}
window.location.href = url;
}
// End -->
</script>
</HEAD>

The cookie is set by a javascript "onload command" Like I said I have it
working on a server with no sub domain.