As to cookies - cookies are scoped by domain so they should work across http:// and https:// boundaries. Cookie support in HttpWebRequest is very minimal however - you need to copy the cookie container. If I remember right the code demonstrates how to do this though or you can look at the West Wind Web Toolkit's HttpClient class which is an update of the original wrapper class.
http://www.west-wind.com/WestwindWebToolkit/docs/page=_3ff0psd7o.htm
It's part of the toolkit that can be found here specifically in the Westwind.Utilities assembly (which is self-contained)
http://www.west-wind.com/WestwindWebToolkit/
+++ Rick ---
http://www.west-wind.com/presentations/dotnetWebRequest/dotnetWebRequest.htm
I was wondering if HTTPS requests are supported, and also mixing both HTTP and HTTPS request with same cookies (session) like mimicking web browsing login to a site, or even making some web service REST API calls that require HTTPS login authentication first before making regular HTTP API calls with some token retrieved from the login step.
If supported, some examples on that might also be helpful. Though I do know that's an old article.