It should as order is important.
4.2 Message Headers
The order in which header fields with differing field names are received is not significant. However, it is "good practice" to send general-header fields first, followed by request-header or response-header fields, and ending with the entity-header fields.
> When sending cookies to a server, all cookies with a more specific path mapping should be sent before cookies with less specific path mappings. For example, a cookie "name1=foo" with a path mapping of "/" should be sent after a cookie "name1=foo2" with a path mapping of "/bar" if they are both to be sent.