You aren't redirecting, right? The browser continues to say www.mydomain.com, it opens a connection with your nginx server which in turn opens a connection to the machine it is actually handling the request, that machine sends its response to nginx and nginx sends it back to the client.
Since nginx is the one actually talking to the client it will need an SSL connection between itself and the client. The internal SSL connection on your network isn't necessarily necessary unless you are worried about your internal networks security.
You'll have to use nginx ssl module. http://wiki.nginx.org/NginxHttpSslModule
server {
server_name www.mydomain.com;
listen 443;
ssl on;
ssl_certificate /usr/local/nginx/conf/server.crt;
ssl_certificate_key /usr/local/nginx/conf/server.key;
location / {
proxy_pass https://192.168.0.1;
}
}
Your current setup probably will work on http://mydomain.com:443 since it is a non ssl connection.