Superheroes that wear hats.

Not masks that wrap the head…hats.

I can think of a few–

[ul]
[li]The Golden Age Sandman[/li][li]The Golden Age Flash[/li][li]The Spirit[/li][/ul]

Can anybody name some more?

Ooo ooo, the Question!

And Rorschach.

The Crimson Avenger.

Vigilante.

Do helmets count?

Politenessman!

Green Arrow

If the power to “cloud mens’ minds” is a super power, then The Shadow works.

Green Hornet
The Shadow
Vigilante (cowboy version)
Phantom Stranger

Define “hat.” Do headbands and tiaras count?

Thor, too.

The Lone Ranger!

The Guardian
The Whip
Doctor Fate
Zatara

Zorro wears a hat over his fashionable black mask.

If Vigilante counts, surely Jonah Hex does too.
Likewise Zatara’s daughter Zatanna.

The original Crimson Avenger
The current Sandman
Uncle Sam
The Bouncing Beatnik
The Fighting Yank

Gads, helmets just open up a whole slew of characters, so I’ll skip them.

No

Yes!

Dark Watcher in City of Heroes

Mandrake the Magician

Captain Action

I think BLACKHAWK and his men would qualify as super-heroes, unlike most military types and LADY BLACKHAWK is currently over at BIRDS OF PREY so add her.