But remember that cookies are stored by the client, and as such are freely modifiable by that client.
For this to be safe, I'd recommend sending another cookie which is a one-way hash of the cookie containing the expiration time, and some secret data known only to the server.
For a bit more on this, check out Encrypted Storage of sensible Data in a Cookie
A golden rule: *Never* trust the data the client gives you without doing some checks on it.
Hope that helps.