The timezone actually shouldn't matter, as HTTP dates are supposed to be in UTC (historically GMT) anyway (cf. RFC7231, sec. 7.1.1.1):
An HTTP-date value represents time as an instance of Coordinated Universal Time (UTC). The first two formats indicate UTC by the three-letter abbreviation for Greenwich Mean Time, "GMT", a predecessor of the UTC name; values in the asctime format are assumed to be in UTC.
Then, the Date
header of the server should be authoritative as the Set-Cookie
header knows no date itself (cf RFC6265, sec. 4.1.1). Your assumption that the next proxy will tack its own Date
header is a bit off. This should only ever happen if the originating server itself has not set one (cf RFC7231, sec. 7.1.1.2):
An origin server MUST NOT send a Date header field if it does not have a clock capable of providing a reasonable approximation of the current instance in Coordinated Universal Time. An origin server MAY send a Date header field if the response is in the 1xx (Informational) or 5xx (Server Error) class of status codes. An origin server MUST send a Date header field in all other cases.
A recipient with a clock that receives a response message without a Date header field MUST record the time it was received and append a corresponding Date header field to the message's header section if it is cached or forwarded downstream.