WebClient wb = new WebClient();
wb.Headers.Add(HttpRequestHeader.Cookie, "somecookie");
From Comments
How do you format the name and value of the cookie in place of “somecookie” ?
wb.Headers.Add(HttpRequestHeader.Cookie, "cookiename=cookievalue");
For multiple cookies:
wb.Headers.Add(HttpRequestHeader.Cookie,
"cookiename1=cookievalue1;" +
"cookiename2=cookievalue2");