Green’s Dictionary of Slang

Smokey n.

also Smokey the Bear, Smoky Bear
[Smoky the Bear, a character used in US fire prevention campaigns]

a traffic policeman, a Highway Patrolman; also attrib.

[US]Chopper Mag. Jan. 42: [headline] BEAR KNUCKLE. Eat Hog, Smokey.
Humboldt Republican (IA) 21 jan. 2/2: Smokey Bear — Any policeman on the highway. Smokey on the ground — Policeman out on patrol. Smokey on rubber — Policeman moving. Smokey dozing — Policeman stopped.
[US]G.V. Higgins Rat on Fire (1982) 89: If there was a Smokey out there tonight, you couldn’t prove it by me.
[US]Eble Sl. and Sociability 21: Smokey the Bear ‘highway patrol officer’.
[US]B. Wiprud Sleep with the Fishes 56: He removed his Smoky Bear hat.

In phrases

Smokey the Bear hat (n.)

(US) a broad-brimmed hat, typically dimpled at the crown, widely worn by U.S. Marine drill instructors, forest rangers, state police, etc.

[US]17 May diary in I. Malloy Southie Won’t Go (1986) 244: The state troopers heralded spring with short-sleeved shirts but not, like last year, their Smokey-the-Bear, wide-brimmed hats.
[US]T.E. Ricks Making the Corps 27: [H]is big flat campaign hat—drill instructors hate it when tourists call it a Smokey the Bear hat.
A. Swofford Jarhead 29: [H]e bashed the brim of his Smokey Bear cover into my nose and pressed his index finger into my chest.