On an existing guest VM (Windows 2003 Enterprise), I'm trying to add a second NIC with host-only type for private network. But on the VM Infrastructure Client, I don't see any option for setting the network type (NAT, host-only, bridge, etc.). Is this feature just not available on ESX? If it's available, how can it be done?
You can create a new vSwitch and do not associate it with any physical NIC's. Then you can assign the virtual NIC to that switch. There is no DHCP by default on the new network so one of your VM's will need to take care of this or you can just manually assign IP's.