A session_id cookie is anything (number or alphanumeric) which identifies a client to a server, which in turns stores (usually temporary) data on the server accessed through this session_id/key.
The point is, if the cookie is going to be passed forth and back over HTTP, it doesn't matter whether you have "signed" it or not. Any man-in-the-middle could get your "signed/encrypted session_id" and make further requests pretending be the proper user. And I mean, this attacker doesn't have to care which information is inside the encrypted data, he could pass the exactly same signed/encrypted data, and the server couldn't figure out if it comes really from the right user.
In cases like these, you have to figure out if the privacy is important, if so, don't think too much, you got have to use HTTPS. If you understand it is not so important, don't waste your "processing time" signing/encrypting and decrypting your session id.
This answer is valid only for signed session_id.