I have two webapps WebApp1 and WebApp2 in two different domains.
As far as I know, cookies are limited by the "same origin" policy. However, with CORS you can receive and use the "Server B" cookies to establish a persistent session from "Server A" on "Server B".
Although, this requires some headers on "Server B":
Access-Control-Allow-Origin: http://server-a.domain.com
Access-Control-Allow-Credentials: true
And you will need to send the flag "withCredentials" on all the "Server A" requests (ex: xhr.withCredentials = true;)
You can read about it here:
http://www.html5rocks.com/en/tutorials/cors/
https://developer.mozilla.org/en-US/docs/HTTP/Access_control_CORS