You can only set a cookie for a domain that's under the current host,
ie. set cookie here :http://perlmonks.org to use at http://perlmonks.org/any/where/on/same/host
When you do not define the domain, the current domain is used as default thus the cookie can be set
So, if corn.com is not under the current domain, the answer is 'No, You can't set the cookie'.

This is obviously for privacy reasons : )