Should I provide an opinion on a graduate school candidate without being asked by the candidate? I've been contacted by email by another professor at a different institution, who is assessing a student for graduate school entry, for an informal opinion about the student's suitability. The student hasn't asked me directly for a recommendation or similar.

Is it ethical for me to provide that informal opinion without informing the student? Does whether the opinion would be positive or negative make a difference?

I'm reasonably sure there are no legal issues involved, so I'm just interested in the ethical considerations.
It does not make a difference whether your review would be positive or negative, and it is your duty to keep your discussions about the student confidential. Should you choose to review their application, you should not tell the student or anyone not involved in the process that you are doing so. 

You are being asked to help your university, or maybe just a professor who trusts you, to help with their admissions and hiring process. You should take it seriously and give an honest review if you can. If you don't feel like you can be objective in your review (maybe the student is a friend or colleague), then you should decline to do so. But I don't feel like there's an ethical issue in the applicant not knowing that you've been asked about them.