We have a small office with one server on SBS 2008 and we don't have a budget right now to buy a new server.
Is it possible to buy a new harddrive, install hyper V then install the latest SBS 2012 and then move over all the data to the new server?
Yes. Use disk2vhd to make an image of your current OS. Put your original hdd aside in case you need it.
Install Hyper-V and import your vhd.
Then, install 2012 in a new VM and run the migration tools. Then, shut down the old VM.