I haven't heard anything. I am running cs3 on Windows 7 and it is fine.
The issue you may run into will come in activating the new installation.
If you only have a single user license then you will have to load up your current CS4 and deactivate that installation.
Adobe tracks software activations online so if you have no more 'activations' then simply installing it and trying to activate it will fail unless you deactivate the 1 you are using.
They will allow you to activate it over the phone in person. I had to do that when a computer died and it wasn't possible to 'deactivate' the software. When I called and explained to customer service they added an activation to my account.