Here's what we know:
* Horatio's loyalty: Horatio is deeply devoted to Hamlet and grieves his death. He is deeply affected by the tragedy that has unfolded, including the deaths of Ophelia, Polonius, and Hamlet's mother.
* Horatio's desire to die: When Hamlet asks him to drink the poisoned cup, Horatio initially refuses but then changes his mind. He says, "I am more an antique Roman than a Dane," suggesting he's willing to die with honor, like a Roman soldier.
* The implications of suicide: It's possible that Horatio sees suicide as a way to join Hamlet in death and avoid the suffering of living without him. However, some scholars argue that he is simply trying to be loyal to Hamlet and share in his fate.
* The poisoning: The poison is meant to kill quickly. Horatio may not have fully considered the implications of drinking it and simply wanted to be with Hamlet in his final moments.
Ultimately, the play doesn't definitively state Horatio's intentions. It leaves room for interpretation, which adds to the tragedy of the story.
It's up to each individual to decide what they believe Horatio's motivations were in those final moments.