Does Halo 2 only work under Windows Vista?
Yes, though there is great potential for installation misery. The top entry of the official Bungie FAQ:
Does Halo 2 Vista work with Windows 7 32-bit/64-bit?
Yes and no. Some people have issues, some people run the game fine. The only way to know is to try yourself.
If you do run into issues, try installing the latest patches (W7, GFWL, and H2) or these workarounds.