I'm assuming that the refurbished MacMini server already has OS X Server (Mountain Lion) installed.
Migrating OD can be done by exporting your users with workgroup manager on the 10.6.8 machine by selecting them and then choose file --> export --> users and importing them using Workgroup Manager 10.8.
I'd migrate first to the 'new' server, test it, and only if it works flawless in your environment -- swap it
After you did this, maybe you can think of another use for your aging iMac? When it meets the requirements, you could also install Mountain Lion and use it as a new workstation, otherwise just use the install disks to install 10.6 and upgrade it to 10.6.8 afterwards.