I know that this has already been answered, but you might like to use this code:
http://snipplr.com/view/4427/
I'm posting it here in case the link goes down at some point:
public static CookieCollection GetAllCookiesFromHeader(string strHeader, string strHost)
{
    ArrayList al = new ArrayList();
    CookieCollection cc = new CookieCollection();
    if (strHeader != string.Empty)
    {
        al = ConvertCookieHeaderToArrayList(strHeader);
        cc = ConvertCookieArraysToCookieCollection(al, strHost);
    }
    return cc;
}
private static ArrayList ConvertCookieHeaderToArrayList(string strCookHeader)
{
    strCookHeader = strCookHeader.Replace("\r", "");
    strCookHeader = strCookHeader.Replace("\n", "");
    string[] strCookTemp = strCookHeader.Split(',');
    ArrayList al = new ArrayList();
    int i = 0;
    int n = strCookTemp.Length;
    while (i < n)
    {
        if (strCookTemp[i].IndexOf("expires=", StringComparison.OrdinalIgnoreCase) > 0)
        {
            al.Add(strCookTemp[i] + "," + strCookTemp[i + 1]);
            i = i + 1;
        }
        else
        {
            al.Add(strCookTemp[i]);
        }
        i = i + 1;
    }
    return al;
}
private static CookieCollection ConvertCookieArraysToCookieCollection(ArrayList al, string strHost)
{
    CookieCollection cc = new CookieCollection();
    int alcount = al.Count;
    string strEachCook;
    string[] strEachCookParts;
    for (int i = 0; i < alcount; i++)
    {
        strEachCook = al[i].ToString();
        strEachCookParts = strEachCook.Split(';');
        int intEachCookPartsCount = strEachCookParts.Length;
        string strCNameAndCValue = string.Empty;
        string strPNameAndPValue = string.Empty;
        string strDNameAndDValue = string.Empty;
        string[] NameValuePairTemp;
        Cookie cookTemp = new Cookie();
        for (int j = 0; j < intEachCookPartsCount; j++)
        {
            if (j == 0)
            {
                strCNameAndCValue = strEachCookParts[j];
                if (strCNameAndCValue != string.Empty)
                {
                    int firstEqual = strCNameAndCValue.IndexOf("=");
                    string firstName = strCNameAndCValue.Substring(0, firstEqual);
                    string allValue = strCNameAndCValue.Substring(firstEqual + 1, strCNameAndCValue.Length - (firstEqual + 1));
                    cookTemp.Name = firstName;
                    cookTemp.Value = allValue;
                }
                continue;
            }
            if (strEachCookParts[j].IndexOf("path", StringComparison.OrdinalIgnoreCase) >= 0)
            {
                strPNameAndPValue = strEachCookParts[j];
                if (strPNameAndPValue != string.Empty)
                {
                    NameValuePairTemp = strPNameAndPValue.Split('=');
                    if (NameValuePairTemp[1] != string.Empty)
                    {
                        cookTemp.Path = NameValuePairTemp[1];
                    }
                    else
                    {
                        cookTemp.Path = "/";
                    }
                }
                continue;
            }
            if (strEachCookParts[j].IndexOf("domain", StringComparison.OrdinalIgnoreCase) >= 0)
            {
                strDNameAndDValue = strEachCookParts[j];
                if (strDNameAndDValue != string.Empty)
                {
                    NameValuePairTemp = strDNameAndDValue.Split('=');
                    if (NameValuePairTemp[1] != string.Empty)
                    {
                        cookTemp.Domain = NameValuePairTemp[1];
                    }
                    else
                    {
                        cookTemp.Domain = strHost;
                    }
                }
                continue;
            }
        }
        if (cookTemp.Path == string.Empty)
        {
            cookTemp.Path = "/";
        }
        if (cookTemp.Domain == string.Empty)
        {
            cookTemp.Domain = strHost;
        }
        cc.Add(cookTemp);
    }
    return cc;
}
This code will read in cookies that are comma separated and correctly parse all parts of each cookie including name, expiration, path, value, and domain.