Reverse Proxy Nginx but cookies don't get through for WP admin

Question

I reverse proxy a blog. It's hosted on Apache under a subdomain blog.example.com. In Nginx I have the following config in a server block.

Everthing works except the cookies for the WP Admin panel don't get passed through so I can't login in.

What should I add?

 location /blog/ {
  proxy_set_header X-Original-Host $host;
  proxy_set_header X-Is-Reverse-Proxy "true";
  proxy_pass_header Set-Cookie;
  proxy_cookie_path / /blog/;
  proxy_pass http://blog.example.com/;
}

Thanks!