Normalde win application cookie desteklemez. Eğer farklı bir amacınız varsa msdn'den aldığım kod işinize yarayabilir.

Msdn'den bir örnek:

[C#] 
using System.Net;
using System;
namespace Examples.System.Net.Cookies
{
    // This example is run at the command line.
    // Specify one argument: the name of the host to 
    // send the request to.
    // If the request is sucessful, the example displays the contents of the cookies
    // returned by the host.

    public class CookieExample
    {   
        public static void Main(string[] args)
        {   
            if (args == null || args.Length != 1)
            {
                Console.WriteLine("Specify the URL to receive the request.");
                Environment.Exit(1);
            }
            HttpWebRequest request = (HttpWebRequest)WebRequest.Create(args[0]);
            request.CookieContainer = new CookieContainer();

            HttpWebResponse response = (HttpWebResponse) request.GetResponse();
            response.Cookies = request.CookieContainer.GetCookies(request.RequestUri);


            // Print the properties of each cookie.
            foreach (Cookie cook in response.Cookies)
            {
                Console.WriteLine("Cookie:");
                Console.WriteLine("{0} = {1}", cook.Name, cook.Value);
                Console.WriteLine("Domain: {0}", cook.Domain);
                Console.WriteLine("Path: {0}", cook.Path);
                Console.WriteLine("Port: {0}", cook.Port);
                Console.WriteLine("Secure: {0}", cook.Secure);

                Console.WriteLine("When issued: {0}", cook.TimeStamp);
                Console.WriteLine("Expires: {0} (expired? {1})", 
                    cook.Expires, cook.Expired);
                Console.WriteLine("Don't save: {0}", cook.Discard);    
                Console.WriteLine("Comment: {0}", cook.Comment);
                Console.WriteLine("Uri for comments: {0}", cook.CommentUri);
                Console.WriteLine("Version: RFC {0}" , cook.Version == 1 ? "2109" : "2965");

                // Show the string representation of the cookie.
                Console.WriteLine ("String: {0}", cook.ToString());
            }
        }
    }
}