If I open winecfg and go to the devices I can change the paths. It works if I choose "/media/windows_c" für the letter C: but Firefox and Thunderbird (I don't test the other here) don't start. I can start other applications like Putty etc. but not Firefox and Thunderbird.
If I change the path at C: to "/media/CORSAIR" (my USB-Stick) Firefox works fine. What can I do that it works on other letters as I, G, P etc.?
Uh, it should work if you launch from your USB stick and SkipCompregFix and SkipChromeFix are false (they are by default) if you don't use the ini. You don't have to worry about drive C: at all. I'm not familiar with winecfg, so I can't give any advice on what your settings should be, but what I wrote above is true with WINE's default settings.
Vintage!