I have been able to run portable versions of Cygwin, reduced in one way or
another, both from writable USB memory sticks and from unwritable CDs.
Lately I tried running XWin from a writable stick. By observing which files
were written where, and as a consequence setting up links using
ln -s /dev/null /tmp/Xwin.log
ln -s /dev/null /var/run/utmp
it really seemed that I had addressed all problems: in repeated uses,
nothing new was written to the stick at all. I then burned a CD, but
disappointingly XWin "dies" as soon as it is started.