The Postman Chrome app does not have access to Chrome cookies - it uses an independent cookie store which is not accessible to Postman, or to the user. We have developed a companion Chrome extension called the Interceptor (https://chrome.google.com/webstore/detail/postman-interceptor/aicmkgpgakddgnaphhhpliifpcfhicfo?hl=en). You can install the Interceptor and enable the Interceptor in Postman to route requests via Chrome. This will ensure that any cookies that saved in Chrome are sent with the request.
Check this blog post for more - http://blog.getpostman.com/index.php/2014/11/28/using-the-interceptor-to-read-and-write-cookies/.
We recommend you switch to the native Postman apps (available at https://www.getpostman.com/apps) for controlling the cookie store. More documentation about this is at https://www.getpostman.com/docs/working_with_cookies.