Bonjour Emanuel,
I know is too late, but I face the same issue latelly.

odoo doesn't seem to specify a domain for cookies, so the requested domain is always used (I guess by the browser). So it's one session per subdomain. 
It might be ok, or not.
If you want to use the same session on every sub domain, you have to set the cookie domain to the parent domain, test dot com in your exemple.
I manage to do this by using this hack on nginx configuration :

# force domain to use parent
proxy_cookie_path / "/;domain=--PARENT-DOMAIN-HERE--";

The session cookie created on either side is shared by both servers, and odoo can read and accept it each time.

I hope it helps !