I do the exact same thing on my dev server(s) so that I can have an rsynced mirror locally and on the off-site server with identical configs.
Here’s what you need in your dnsmasq.conf (make sure you restart it) assuming your webserver’s internal interface is 192.168.0.3:
address=/.server.mydomain.com/192.168.0.3
This will create a wildcard entry for *.server.mydomain.com and as long as your client’s are using DNSMasq for their DNS (and your server listens in the internal interface), you’re set.