Yeah, this is probably tricky.
First thing - you need your existing users to be input into the threads database - they would have to have a user entry in the w3t_Users table. That's why doing the reverse and using threads for the registration system is much easier.
So you'd need to copy your existing users to the Threads database and modify your existing new user function to also add users to the Threads database.
Passwords need to be stored MD5 encoded in the w3t_Users database, and some other key fields need to be setup U_Approved = 'yes' etc.... You can check the INSERT function inside the adduser.php for exactly what the minimum info is needed to insert the user.
Then indeed, you'd need to replicate the cookies that are set when you login to threads. You can see this in the ubbt.inc.php in the function "do_login".
If your existing pages handling this are php and using MySQL it would be easier to replicate what the login function does, and even perhaps include the main.inc.php file so that your pages have access to the threads variables etc...
Assuming you're using cookies.... I'm not exactly sure how it would need to be handled in Sessions.
I've never done anything myself this way, I've done it the way omegatron suggests, getting other PHP pages etc.. to work off the Threads user base.
I would presume it's more complicated if your existing pages are not PHP pages. I'm not sure, as I'm not proficient in other languages.