He is Danish. He knew Hamlet Sr. by sight (he says the ghost looked like him), he made a point of coming to his funeral, and most telling, he refers to him as "our king". Barnardo and Marcellus know him well enough to ask him to see the ghost. When Hamlet goes to England, Horatio stays and is on intimate terms with the Queen. When letters come by sea to him, he says "I do not know from what part of the world I should be greeted, if not from Lord Hamlet." This is unlikely as it is, since we know he has fellow-scholars at Wittenberg, but would be impossible if he had grown up in some other country.
There is a counter-indication when he asks Hamlet, "It is a custom?" Surely if he had been hanging around the Danish royal court that much, he would know.
Horatio - Hamlet - was created in 1600.
Hamlet asks Horatio to, "tell my story"
Horatio plans to go meet Hamlet at Elsinore, which he does in Act 1 Scene 2. Horatio plans to meet Hamlet on the battlements, which he does in Act I Scene 4. Horatio plans to meet Hamlet at the play, and does in Act 3 Scene 2. Horatio has no plans to meet Hamlet in England.
Hamlet: My father! Methinks I see my father! Horatio: Where, my lord? Hamlet: In my mind's eye, Horatio.
Not Denmark. Horatio is unfamiliar with the customs in Denmark: when Claudius first starts his trumpet and cannon accompaniment to his drinking, Horatio asks "Is't the custom?" whereupon Hamlet replies that it is but "to my mind though I am native here and to the manor born, it is a custom more honoured in the breach than the observance." If Horatio had been Danish he would have known that this was a custom. Horatio and Hamlet met at University in Germany: Horatio may be German.
Hamlets friends are Rosencrantz, Guildenstern and Horation. However throughout the play Rosencrantz and Guildenstern turn against Hamlet (not going to spoil how!) which leads to their downfall. Horation never goes against Hamlet, he is always there for him when Hamlet needs him. Hamlet is the best play by Shakespeare!!
Horatio is Hamlet's friend from university. He tells Hamlet that his father's ghost has been seen wandering the castle walls.
Hamlet prevents Horatio from drinking what's left of the wine that Claudius poisoned, because Hamlet wants Horatio to tell people his side of the story.
Hamlet asks Horatio to observe Claudius.
Elsinore
Horatio finds Hamlet asleep in the middle of a dirt road.
Hamlet's friend Horatio is a student.