Вы ищете что-то подобное?
//Convert to string
HttpCookieCollection source = new HttpCookieCollection();
string result = source.Cast<HttpCookie>().
Aggregate(string.Empty, (current, cookie) =>
current + string.Format("{0}={1} ", cookie.Name, cookie.Value));
//Convert back to collection
HttpCookieCollection dest = new HttpCookieCollection();
foreach (var pair in result.Split(' '))
{
string[] cookies = pair.Split('=');
dest.Add(new HttpCookie(cookies[0],cookies[1]));
}