Let's look at the context here. The Danes are preparing for what they think will be an imminent invasion by the Norwegian army under Fortinbras. The atmosphere is tense and there's a great deal of gloom and foreboding in the air. When the ghost of Hamlet's father appears on the battlements of Elsinore it merely adds to the sense that something bad's about to happen.
That's certainly how Horatio interprets this strange apparition. He's normally a very rational, sensible man, but even he's spooked by what appears to be a bad omen. Initially skeptical, once he's seen the Ghost he immediately sees its resemblance to old King Hamlet. He doesn't know quite what the Ghost's manifestation portends, but he knows that, whatever it is, it can't be good. Horatio has no idea just how right he is.