Cookies are handled by the browser. With RestGWT you are sending Ajax requests from your javascript application code. So if you need to pass the value of your cookie to your ajax request you need to retrieve it first then add it manually to your RestGWT request by using a Dispatcher for example.
To retrieve the cookie value value can use com.google.gwt.user.client.Cookies
Then to add you cookie value to your RestyGWT query you can use a Dispatcher org.fusesource.restygwt.client.Dispatcher