I mean, would you recommend to set cookies with domain mysite.com and thus have a different domain for external services, like support.mysite.net, or...? (genuinely asking, I don't mean to criticize, sorry if the english is not perfect :)
www.mysite.com
support.mysite.com
wordpress.mysite.com
You could use *.secure.mysite.com for all internal apps, but that seems ugly. You could also not use subdomains for any internal apps, like Google, but that's limiting in other ways - notably, it makes it impossible to have any security isolation between internal apps.
Issue a master session cookie at login.mydomain or account.mydomain. If your user hits a subdomain and is not logged in, forward them there (in the background) and see if you can grant them a redeemable token for the round trip. If so, they can get a cookie issued by the subdomain in exchange for the token when they return.
I guess there is still some tricks when the user lands in a subdomain and needs to be redirected to another, e.g. www -> mobile, but I'll figure out the details :)