Will Adobe CS3 and earlier run on 10.8

I'm not sure if they will run or not...I have CS5 and that works on mine, however, you do not need to upgrade to Lion before going to Mountain Lion...If you already have Snow Leopard which you stated you did, you can skip over Lion and go straight to Mountain Lion (10.8)

Photoshop CS3 system requirements

Mac OS

PowerPC G4 or G5 or multicore Intel processor

• Mac OS X v10.4.8-10.5 (Leopard)
• 512 MB of RAM
• 64 MB of video RAM
• 2 GB of available hard-disk space (additional free space required during installation)
• 1,024 x 768 monitor resolution with 16-bit graphics adapter
  
• DVD-ROM drive
• QuickTime 7 software required for multimedia features
• Internet or phone connection required for product activation
• Broadband Internet connection required for Adobe Stock Photos* and other services

I think your CS3 is just to old. I upgraded mine to be compatible with OS 8. (I agree with skipping OS 7)

CS3 will run on ML, except for Droplets (which won't) I still use it and never usd droplets even when they did work.