If the XML document has an XML declaration with an encoding specified
then xmlDocument.FirstChild is the XmlDeclaration node and has a
property named Encoding:

      XmlDocument xmlDocument = new XmlDocument();
      xmlDocument.Load(@"file.xml");
      if (xmlDocument.FirstChild.NodeType == XmlNodeType.XmlDeclaration) {
        Console.WriteLine("Encoding is: \"{0}\".",
((XmlDeclaration)xmlDocument.FirstChild).Encoding);
      }
      else {
        Console.WriteLine("No XML declaration found.");
      }