It would help if we knew how you were setting the cookies. Note that NRNR's response is a bit misleading - he/she's right about the domain, but there's no requirement to set an expiration. However you will get varying results unless you explicitly set a path too - even if it's just '/'.
Browsers do vary a lot in how they handle all sorts of things, including cookies - so I wouldn't be too surprised if there are browsers out there which start retrieving additional content before the response headers for the referencing html page are processed. This is not how its supposed to work though.
C.