You're asking if Adobe Creative Suite (ACS, I assume) runs on Windows? That's funny because I nearly always see it running on Windows, once or maybe twice I've seen it on OSX. If this is actually an important tool for you I really doubt you'd ask this question as you would have seen examples and documentation relating to Windows. I think you're feigning ignorance.
I think there was a time where multimedia programs did not work well under Windows, but at least since XP things have gotten very usable (and acceptably stable with 7+). In fact, although I will kick and scream in anger if you try make me use proprietary software - I'd rather use ACS on Windows because then you at least get a logical interface and usable file manager (without resorting to BASH in OSX).
I'll probably blow some people's minds here: not all design tools under Linux are bad. For some areas of design they can actually be used seriously - Scribus for layout and Inkscape for vector graphics. There are even many professional places that use Blender for 3D modelling (though Blender can do other things too). There are also some proprietary design tools which run under Linux too, but they're of little interest to me so I can't comment.
As an aside, with the amount of times I have heard ACS for Linux requested by professionals I am really surprised Adobe has not gotten their act together and taken the opportunity to make a bunch of money from re-selling their products on this platform.