In W3TC you can specify files or cookies that are ignored and not cached.
Exclude Files from Cache
To do this go to WordPress Admin > Performance > Page Cache
In the screenshot … you will see I’ve added custom sidebars from a Twenty-Eleven theme. These are excluded from being cached.
You can also specify your custom cookie to not be cached …
Browser Cache Settings
BUT also check your Browser Cache settings as you’ll probably want to reduce these from 1 year to 1 month or week or day.