I'm doing a lot of website design and I'm looking for a feature that would allow me to set the main colors of website in variables and use the variables in color overlays and such.
It would make changing the color scheme of site a lot easier and that would help previewing different possibilities. So, does such feature exists, or is there some kind of plugin for it? I'm using CS3 and I have CS4 available if it's required for this.
I don't think that exists, but you could use Hue/Saturation adjustment layers with a mask...
This doesn't answer your question directly, but being able to change colour values readily is one of the advantages of working directly in HTML/CSS as much as possible.
See this article: 24 Ways: Make Your Mockup in Markup which discusses new CSS3 features which, if not usable yet in production sites due to limited wide browser support, can be used for making more sophisticated code-only prototypes.
If you were using Illustrator rather than Photoshop, "Global" colours used in the artwork could be redefined in the palette.
Photoshop can be scripted via AppleScript, VBScript, and Javascript, so you should be able to do what you want. See my answer to this question for more info.
This is something which Illustrator would be much better suited for, but you can kinda pull it off with spot channels.
