Maybe it’s lines like this that make people feel that Horatio is close to Hamlet, After all. Who but your closest friend would tell you this kind of truth? But – if we look a little closer, we see that Horatio is speaking to Hamlet in a very formal manner. He’s calling him “you” not “thou” and calling him “my lord” – not “my friend.” Granted, Hamlet is a prince and there aren’t many who could or should risk getting informal with him. Horatio switches to the thou form once he’s dead.
Of course, he also attempts to poison himself once it becomes clear that Hamlet’s on his way out the door – so that suggests a strong bond, for sure.
Though, it may be self preservation – to be the only one left living in a total bloodbath does rather make one look a bit…guilty.
I’m not saying that’s why Horatio brings up his antique Roman tendencies but it may be out of something apart from friendship – and he could have switched to something a bit less formal here if he’d wanted to, even if he kept using you. He could have called Hamlet something more affectionate than “my lord.” Though, perhaps the formality allows truth to be spoken.