Does AW use cookies from domains other than absolutewrite.com?
Nope.
There are, I think, three for the forums.
And there's one for the WordPress blog.
The AW forum cookies serve as a token for identifying you, so you don't have to re-enter your login each time, if you have the Remember Me box set, they track your read/not read progress and then send it to the database (so you are up to date on any web browser/computer you in from and don't see things you've already read).
ETA: If you go to a passworded forum, each one of those adds a cookie. There are some other special purpose cookies--but all are clearly labeled.
If you've been a member a long time and not deleted AW cookies, you will have old cookies from previous versions of the forum software, too.
If you want me to go spelunking in a bit and be precise, I will, but I'm on a bit of a deadline at present.
They are also set to automatically self-destroy so if someone hasn't logged in in a while the cookie becomes "stale."