Secure cookies and mixed https/http site usage
Solution 1:
The solution you propose seems like it would work, as long as you don't mind non-authorized people being able to view the non-secure (http) part of the site 'as if they are logged in' - ie as long as the http part of the site does not contain any sensitive information, and the only difference between logged in and not-logged-in users is something harmless in the header.
The reason it is not used very often may be one of:
- This scenario may just not be very common. Usually if you care enough to make part of your site secure, you'd restrict the login session just to that secure part, or you'd make the entire site always use HTTPS (like Paypal).
- Pre-existing solutions exist which are secure and which are capable of more than this, for example logging in someone at an HTTPS login form and maintaining that session while transferring them back to HTTP.
OpenID's an example. Also think flickr or gmail: their sign in page is always HTTPS, but once the session's started you migrate back to HTTP while maintaining the session securely.
Update (Aug 2014)
Since I wrote this back in 2009, the practice of having a secure connection for the login screen but dropping back to HTTP once logged in has all but disappeared.
The overhead of using HTTPS side-wide is not seen as much of a big deal anymore. The new SPDY protocol pioneered by Google (now evolved into HTTP/2) is supported cross-browser and by major web servers and improves HTTPS speed.
And lastly, privacy is seen as more important than ever, even for actions that aren't critical to the authentication, such as writing comments, uploading photos, and more.
Google has even said recently that sites which are HTTPS-only will start to benefit in search engine rankings.
Solution 2:
From a security standpoint, you should never trust any content sent over a non-secured connection. So with that in mind, then it is safe to use a cookie sent over an unencrypted connection only if the cost of theft or misuse of that cookie is approximately zero.
With that in mind, most sites are designed such that the data isn't allowed to "leak" between the channels. After all, data coming from the encrypted side is usually privileged, and therefore shouldn't be allowed in the normal channel, while data coming from the unencrypted channel is potentially spoofed, and shouldn't be trusted.
If you have data that doesn't fit those generalizations, then feel free to do with it as you please.