Adobe has posted a .pdf outlining the current state of compatibility between Snow Leopard and their products:
Working closely with Apple, Adobe has tested and determined that our Adobe Creative Suite 4 products and components are compatible with Mac OS X Snow Leopard.
[…]
Older versions of Adobe creative software were not included in our testing efforts. While older Adobe and Macromedia applications may install and run on Mac OS X Snow Leopard (v10.6), they were designed, tested, and released to the public several years before this new operating system became available. You may therefore experience a variety of installation, stability, and reliability issues for which there is no resolution. Older versions of our creative software will not be updated to support Mac OS X Snow Leopard (v10.6).
In my experience, CS3 runs just fine under Snow Leopard, but older users, be aware you may come across some bugs.