foobar.com never has access to cookies from google.com. when requests are sent to google.com, cookies are added. when you load google.com, JS can access the google.com cookies.
google analytics: google.com tracking cookie is to identify the user. the js in the page knows the current website and tells google "im here". the dominance of google analytics and adsense means users are tracked wherever they go (because google is always there and recording)