The Short Answer - You cannot read the cookie's expiration date and time.
The browser is responsible for managing cookies, and the cookie's expiration time and date help the browser manage its store of cookies. Therefore, although you can read the name and value of a cookie, you cannot read the cookie's expiration date and time. When the browser sends cookie information to the server, the browser does not include the expiration information. (The cookie's Expires property always returns a date-time value of zero.)
You can read the Expires property of a cookie that you have set in the HttpResponse object, before the cookie has been sent to the browser. However, you cannot get the expiration back in the HttpRequest object.
If you really want to get the expiration, then you'd have to store it in the cookie itself: