You can use X forwarding by specifying a flag in the ssh command: "ssh -Y ..." or "ssh -X ...". All traffic is forwarded through the SSH connection, so if you can use SSH now then you can use X forwarding. X forwarding will allow you to start individual X apps from the prompt, but not the whole desktop environment. Also X forwarding is somewhat slow over the Internet.
If you want to get a remote desktop type of thing, you can use VNC. Most Linux distributions come with RealVNC and/or TightVNC, etc. Set up the VNC server on your home computer, and use a VNC client to connect to it.