He is a hero.
The whole play is a "morality" play, with a virtue/vice comparison between Falstaff and Hotspur. But the twist is, from the outset, that Falstaff is really the virtue (wise, biblical, popular), while Hotspur is lost in vanity (harebrained, hot blooded) - but brave and honourable, like a legendary giant, with a devout, idealistic maiden in tow:
Prince Hal: ...I am not yet of Percy's mind, the Hotspur of the north, he that kills me some six or seven dozen of
Scots at a breakfast, washes his hands, and says to his wife “Fie upon
this quiet life! I want work.” “O my sweet Harry,” says she, “how many
hast thou killed today?” “Give my roan horse a drench,” says he, and
answers “Some fourteen,” an hour after. “A trifle, a trifle.". Act 2, Scene 4.
Hotspur is chivalry, and is considered on the whole to be living up to the expectation of his time. But, ultimately, in vain:
Falstaff: ...There's honour for you! Here's no vanity! Act 5, Scene 3.
and slightly earlier
Falstaff: What is honour? A word...Honour is a mere scutcheon - and so ends my catechism.
Act 5, Scene 1.
He is definitely not a villain. Perhaps there is similarity to Hamlet, who is lost in vain. Also, for his hot-bloodedness, I can see similarities with Sonny in The Godfather:
Clemenza: I hope you're not a hot head like your brother Sonny, you
can't talk business with him. The Godfather.
Is Sonny a villain in the Godfather? No way.
Perhaps Hotspur's actions are not on the whole "recommended" by Shakespeare, in some sense, but he is given the role of a hero, not a villain. It is more likely Falstaff is the villain. Consider Henry IV Part 2, where Falstaff is ultimately cast out, and Henry V, where Bardolph is hanged. But then, he is too likeable. So there is a deep character comparison going on. If there is a villain, what is being driven out is Hal's un-kingly life. He is fulfilling his potential. So personalities are so bright and vivacious in the play, it is the opposite (dullness) which is being driven out "with a dagger of lath", leaving the fulfilment of Hal as Henry V (again, like in the Godfather).