The exception happens later on, when the response from Google is to be loaded by the XmlDocument. And Google uses a different encoding for the English and Arabic response, resp.: ISO 8859-1 for English, and Windows-1256 for Arabic.
Following code works on my computer with both requests:
XmlDocument doc = new XmlDocument();
HttpWebRequest request = (HttpWebRequest)WebRequest.Create("http://www.google.com/ig/api?weather=amman&hl=ar");
HttpWebResponse response = (HttpWebResponse)request.GetResponse();
Stream resStream = response.GetResponseStream();
System.IO.StreamReader reader = new System.IO.StreamReader(resStream);
doc.Load(reader);