I'm wrestling with the same stuff, sending logins via https on a different host (and domain, and server!). I found a way...
Say both subdomains are on the same box:
www.host.com -> /home/host_www/web
www2.host.com -> /home/host_www2/web
1: Create a folder eg
/home/host_www/sessiondata
with chmod 777
2: At the top of any scripts which need the session ID, in either subdomain, do
ini_set('session.save_path',"/home/host_www/sessiondata");
Then your session data should be common across both hosts/subdomains.
You could make this more secure by using more limited permissions on the sessiondata, if you know more about permissions than I do.
If the subdomains are NOT hosted on the same box, it's more difficult - I think I have a solution, if anyone wants it.
NB - I think this works, but I've only just tried it on php4.2.2 - there may be issues with other versions, or aspects I haven't tested. Caveat Programmor. 🙂
nik