Many traditional superheroes in comics don't have superpowers. But that does not demean their superhero status.
Merriam-Webster defines "superhero" as "a fictional hero having extraordinary or superhuman powers." Intuitively, though, that seems incorrect. One of the most famous superheroes of all, Batman, has no powers to speak of, but still wears a mask and a cape, has a secret identity and prowls around his town at night looking for bad guys to beat up. Pretty much the superhero job description, right?
The dictionary continues, "also: an exceptionally skillful or successful person." Bruce Wayne is certainly both, though the relative ambiguity of the supplementary definition implies that any exceptionally skillful successful person could be considered a superhero, cowl or not. (Oprah Winfrey, superheroine?)
It's also important to look at the situations Batman, the most prominent powerless costumed crime-fighter, finds himself in he's frequently fighting aliens and otherworldly beings, he built the Justice League an outer space hangout, and there's an entire comic book series dedicated to his team-ups with Superman. It's amazing he has time to chase Two-Face out of abandoned Gotham City warehouses.
Clearly, Batman is more than compensating for his lack of powers with his superhero-like behavior. But not every powerless costumed crimefighter is a superhero. Take Marvel Comics' the Punisher, who also uses only his intellect (and a copious amount of guns and ammo) to fight crime, but usually does so solely against street-level thugs and mobsters.
There's a whole class of DC Comics and Marvel characters that are superheroes merely by virtue of being really good at something, commonly archery. Green Arrow, his Marvel counterpoint Hawkeye, and Green Arrow's many associates and proteges (Arsenal, Speedy, Arrowette) all manage to be superheroes simply by being handy with a bow.
Marvel's Shang-Chi is just a uniquely proficient martial artist. Then there's DC's Mister Terrific powerless, but as his name not-so-subtly suggests, is terrific at just about everything.
Then there are the superheroes who have no powers themselves, but utilize a device of some kind that allows them to do superhuman things. Iron Man is the most famous example he's just a guy in a suit. (Sure, there was a story in the comics recently where part of the suit was actually inside his body, and he could control it with his mind, but that's over now.) Green Lantern is another an average dude without his power ring, but nearly limitless in power with it on.