Is the authentication cookie sent back under HTTPS?

Hi Folks,

I've created at "Hotmail" type login method - where a user enters their password under HTTP - but the form is posted to a "login.aspx" page under HTTPS...
The "Login.aspx" page validates user credentials and then redirects the user back to the original page he was on under HTTP.

My question is...is the authentication cookie sent to the browser via HTTPS or not?
I'd like the cookie to be issued under HTTPS...but I'm not sure at what point the server sends the cookie back, to the browser:

Is it while the user is under https://mydomain.com/login.aspx           <-- this would be good!
Or  when the browser is redirected to http://mydomain.com/myformerpage.aspx  <-- this would be bad!
(Url's for example only..!)

This is t ...