No, Hyper-V Server 2012 doesn't expire.
Hyper-V Server is quite a bit like Server Standard Core with all of the roles except Hyper-V (and other supporting roles and features) removed.
Now, in Server 2012, you can add the full UI back to the Server Core editions, but that's not an option with Hyper-V Server 2012 - it will always just be a command-line. That also means that the typical management UI tools won't run on Hyper-V Server 2012, so you'll need a machine that you can manage it from remotely (the PowerShell cmdlets for Hyper-V actually do work on Hyper-V Server, though).
Hyper-V Server isn't really for people who want to "play around" with Hyper-V - it's really designed for people who want to boost their Hyper-V infrastructure with more physical hosts, and who want to run a very lightweight OS in the root partition, leaving the most resources available for the VMs.
If you just want to get used to Hyper-V or test some things out with it, but you don't have experience with managing Hyper-V remotely already, stick with a full version of Windows Server (or Windows 8 Pro/Enterprise x64, which also have Hyper-V).