Cookie handling is not related to how you render views. In case of SSR, the browser will still send an HTTP request to load a view, which means cookies will be automatically sent to server as a part of request header.
it's simpler for browsers to send cookies by making them share domains. But it's tricky to send Cookies from that render server to a original data server, since we probably use a same copy code Ajax code on both side. Well, using two copies of code can be a solution, but tedious enough to write that twice. Like described in @pluma 's answer.