Hello Tim.
Yes, you can use cookies with MQX. It really has nothing to do with MQX though. I use a Javascript function to store the cookies, and then one to retrive the cookies. On a page load, I call "getCookie()" for each of the variables that I want restored from the web browser's cookie store, and when necessary, I call "setCookie()" to store them off in the browser. Once you've restored the cookies to a Javascript variable, then you could push that value to a hidden form field, or append the values in your html request string to send it to your MQX functions for parsing.
I use the exact functions from this page: http://www.w3schools.com/js/js_cookies.asp
Good luck,
Neil