Para implementarla solo tenemos que crear una clase que herede de System.Web.Services.Protocols.SoapExtension. Aquí tienes un ejemplo sacado de la documentación de MSDN, intercepta los mensajes en la entrada duespues de serializar (Paso 2 en el gráfico) y en la salida antes de Deserializar (Paso 4 en el gráfico) y guarda los mensajes en disco.

public class TraceExtension : SoapExtension
{

    Stream oldStream;
    Stream newStream;
    string filename;

    // Save the Stream representing the SOAP request or SOAP response into
    // a local memory buffer.
    public override Stream ChainStream( Stream stream ){
        oldStream = stream;
        newStream = new MemoryStream();
        return newStream;
    }

    // When the SOAP extension is accessed for the first time, the XML Web
    // service method it is applied to is accessed to store the file
    // name passed in, using the corresponding SoapExtensionAttribute.
    public override object GetInitializer(LogicalMethodInfo methodInfo,
	                                   SoapExtensionAttribute attribute)
    {
        return ((TraceExtensionAttribute) attribute).Filename;
    }

    // The SOAP extension was configured to run using a configuration file
    // instead of an attribute applied to a specific XML Web service
    // method.
    public override object GetInitializer(Type WebServiceType)
    {
      // Return a file name to log the trace information to, based on the
      // type.
      return "C:\\" + WebServiceType.FullName + ".log";
    }

    // Receive the file name stored by GetInitializer and store it in a
    // member variable for this specific instance.
    public override void Initialize(object initializer)
    {
        filename = (string) initializer;
    }

    //  If the SoapMessageStage is such that the SoapRequest or
    //  SoapResponse is still in the SOAP format to be sent or received,
    //  save it out to a file.
    public override void ProcessMessage(SoapMessage message)
    {
        switch (message.Stage) {
        case SoapMessageStage.BeforeSerialize:
            break;
        case SoapMessageStage.AfterSerialize:
            WriteOutput(message);
            break;
        case SoapMessageStage.BeforeDeserialize:
            WriteInput(message);
            break;
        case SoapMessageStage.AfterDeserialize:
            break;
        default:
             throw new Exception("invalid stage");
        }
    }

    public void WriteOutput(SoapMessage message){
        newStream.Position = 0;
        FileStream fs = new FileStream(filename, FileMode.Append,
                                       FileAccess.Write);
        StreamWriter w = new StreamWriter(fs);

        string soapString =
          (message is SoapServerMessage) ? "SoapResponse" : "SoapRequest";
        w.WriteLine("-----" + soapString + " at " + DateTime.Now);
        w.Flush();
        Copy(newStream, fs);
        w.Close();
        newStream.Position = 0;
        Copy(newStream, oldStream);
    }

    public void WriteInput(SoapMessage message){
        Copy(oldStream, newStream);
        FileStream fs = new FileStream(filename, FileMode.Append,
                                       FileAccess.Write);
        StreamWriter w = new StreamWriter(fs);

        string soapString = (message is SoapServerMessage) ?
                            "SoapRequest" : "SoapResponse";
        w.WriteLine("-----" + soapString +
                    " at " + DateTime.Now);
        w.Flush();
        newStream.Position = 0;
        Copy(newStream, fs);
        w.Close();
        newStream.Position = 0;
    }

    void Copy(Stream from, Stream to)
    {
        TextReader reader = new StreamReader(from);
        TextWriter writer = new StreamWriter(to);
        writer.WriteLine(reader.ReadToEnd());
        writer.Flush();
    }
  }
}

Para poder insertar la SoapExtension en la entrada y salida de un WebMethod hay que crear una clase que herede de SoapExtensionAttribute cuya propiedad ExtensionType le dice al framework que clase SoapExtension utilizar. También tiene una propiedad Priority para que en caso de que haya más de un SoapExtension el sistema sepa en que orden ejecutarlas:

  // Create a SoapExtensionAttribute for the SOAP Extension that can be
  // applied to an XML Web service method.
 [AttributeUsage(AttributeTargets.Method)]
 public class TraceExtensionAttribute : SoapExtensionAttribute {

   private string filename = "c:\\log.txt";
   private int priority;

   public override Type ExtensionType {
       get { return typeof(TraceExtension); }
   }

   public override int Priority {
       get { return priority; }
       set { priority = value; }
   }

   public string Filename {
       get {
           return filename;
       }
       set {
           filename = value;
       }
   }

Para que un WebMethod utilice la SoapExtension solo queda aplicar el SoapExtensionAttribute al método:

[WebMethod]
[TraceExtension()]
public string MetodoWeb(string str)
{
    return "Hola";
}