How to properly configure BIND forward zone for an internal DNS server?

Add a 'forward only;' statement to the forwarded zone:

zone "subzone.mydns.example.com" {
    type forward;
    forward only;
    forwarders { 192.168.0.4; };
};

I did and other step more, the first one mentioned by @brandon-xavier:

zone "subzone.mydns.example.com" {
    type forward;
    forward only;
    forwarders { 192.168.0.4; };
};

and the new one:

$ORIGIN subzone.mydns.example.com.
@             IN      NS      ns1.subzone.mydns.example.com.

But I don't know why it is neccesary...

You have to configure the A RR for the NS "subzone.mydns.example.com." on your external DNS. It's named "glue record" and will correspond to the IP of your internal DNS. Currently, your external DNS is not capable to known the IP of the internal DNS. Regards