I just ran a test that shows that the conversion is made from server time zone to client time zone. However, if the client time is off by a few minutes, then the cookie can hang around for a few, or die a few minutes too soon. The source code for the test is
in the Sandbox.
For absolute accuracy, you would need nab the client time and time zone, then convert the client time to the server time zone.
let me know if you nab the client time and time zone.
btw, you could just store the server time in a cookie and check for expiration yourself.