From http://www.twilio.com/docs/api/twiml/your_response:
Twilio behaves just like a web browser when making HTTP requests to URLs:
Cookies: Twilio accepts HTTP cookies and will include them in each request, just like a normal web browser.
Redirects: Twilio follows HTTP Redirects (HTTP status codes 301, 307, etc.), just like a normal web browser.
Caching: Twilio will cache files when HTTP headers allow it (via ETag and Last-Modified headers) and when the HTTP method is GET, just like a normal web browser.
However, if I set a cookie, then issue a redirect using the verb, will the end point (a different IP) be able to retrieve the cookie I set prior to redirecting?
Docs on redirect verb:
http://www.twilio.com/docs/api/twiml/redirect
No. Cookies are scoped to a domain or IP address (just like your browser) and cannot be read across different domains. You will need to write your own storage code and have independent data storage (like a database) that can be accessed from both locations to share state.