[Deque]

You forgot to close your streams. Close them within a finally block.

Don't use EXIT_ON_CLOSE, but DISPOSE_ON_CLOSE instead. The latter will shut down your program just fine if it was the last window and you have nothing else going on (like an indefinite loop).
EXIT_ON_CLOSE is the sledgehammer method to shut down your program. It just kills the JVM making your program unembedable, impossible to do some cleaning up before shutdown (like autosave, removing temp files) and makes it hard to test (because the testing methods won't work anymore if you shut down the JVM).

Don't catch all exceptions by using the most general Exception class, catch only the ones that are actually thrown there.

Your ArrayList is missing a type parameter. You probably get a warning for that, don't you? Same for the Iterator.

Instead of using iterators to iterate through the list you can use the foreach loop of Java. Looks a bit cleaner:

Code:

for(Writer writer : clientOutputStream) { //do stuff }

I am missing a possibility to shut down the server properly (and get out of this neverending while loop).

The name clientOutputStream is misleading. It is a list and you have possibly several writers in there, so it would be more appropriate to use the plural form.
Furthermore the elements in it are no OutputStreams, but Writers that use an OutputStream to write to.

Make the fields of your classes private (unless it is appropriate to make them public, like for constants which should be used by other classes, but in most cases they should be private).