I'd like to allow my users to opt-in to a new version of my website. Is there any way to make my domain point to a different DocumentRoot within my virtualhost configuration if a user has a particular cookie set? Or is there any other way to achieve the same result without having to setup varnish, nginx, etc?
A cookie redirection would probably be the most efficient method. Set up the new website either inside of a new directory, or inside of a virtualhost with a different hostname prefix. Redirect them to the new location based on the presence of the cookie.
This looks like it may be close to what you want: http://david.narrabilis.com/node/40