The implementation of a http cookie is leaky. Better get used to it. You can read RFCs about, but better read one, more meaningful question posted on the security stackexchange. If your site is hosted as a subdomain with others apps and a malicious user can access any other app a cookie with top domain can be set. What it means, is that the cookie will be sent with every request to the top domain as well as yours (domain-match verb in the RFCs). This can bring a lot of trouble when an attacker sets a cookie with a name important for your app, like a session cookie. According to the specification, both values will be sent under the same name with no additional information about on which basis a given value was sent.
Html5 to the rescue
If you design a new Single Page Application, you can be saved. Imagine that during POST sending the login data (user & password) in a result JSON a value previously stored in cookie is returned. One can save it in the localStorage easily and add later on to the headers of requests needing authentication. A simple change brings another advantage. Requests not needing authentication like GETs (as noone sends fragile data with verb that is vulnerable to JSON Hijacking) can be sent with no header overhead to the same domain. A standard solution to stop sending cookies with GETs is shipping all your static files to another domain. That isn’t needed anymore.