Douglas Harper's Etymology Dictionary
"state policeman," 1974, from truckers' slang, in reference to the wide-brim style of hat worn by state troopers (the hats so called by 1969). Ultimately the reference is to a popular illustrated character of that name, dressed in forest ranger gear (including a hat like those later worn by state troopers). He was introduced in 1944 by the U.S. Forest Service and the Wartime Advertising Council in a campaign to lower the number of forest fires in the West.
Wikipedia
Smokey Bear (also called Smokey the Bear) is an American advertising mascot created to educate the public about the dangers of forest fires. An advertising campaign featuring Smokey and the slogan "Smokey Says – Care Will Prevent 9 out of 10 Forest Fires" was created in 1944. Smokey Bear's later slogan, "Remember... Only YOU Can Prevent Forest Fires" was created in 1947 by the Advertising Council. In April 2001, the message was updated to "Only You Can Prevent Wildfires." According to the Ad Council, Smokey Bear and his message are recognized in the United States by 95% of adults and 77% of children.
In 1952, the songwriters Steve Nelson and Jack Rollins had a successful song named "Smokey the Bear". The pair said "the" was added to Smokey's name to keep the song's rhythm. During the 1950s, that variant of the name became widespread both in popular speech and in print, including at least one standard encyclopedia. A 1955 book in the Little Golden Books series was called Smokey the Bear and Smokey calls himself by this name in the book. It depicted Smokey as an orphaned cub rescued in the aftermath of a forest fire. From the beginning, Smokey's name was intentionally spelled differently from the adjective 'smoky'.
The fictional character Smokey Bear, created by the art critic Harold Rosenberg, is administered by three entities: the United States Forest Service, the National Association of State Foresters, and the Ad Council. Smokey Bear's name and image are protected by U.S. federal law, the Smokey Bear Act of 1952 (16 U.S.C. 580 (p-2); 18 U.S.C. 711).
Usage examples of "smokey bear".
She was small, only a little taller than I, thin, with close-cropped hair hidden under her Smokey Bear hat.
His Smokey Bear hat shielded his face but left his ears and the back of his head open to the cold.
You became Smokey Bear's right-hand man and you've never looked back.
His Smokey Bear hat was pulled low over his head, thick woolly collar pulled up near his chin.
The passenger door opened, and a beefy man in tans, wearing mirrored sunglasses and a Smokey Bear hat, got out and came toward him.
It bore the brown symbol of the forest preserve department, the ranger's hat, Smokey Bear's, used by all the days.
Anna said, setting her Smokey Bear hat squarely on her head and taking a last look around quarters she hoped soon would be hers.
I don't know exactly what the score is here, but it might be best if I wasn't seen arriving in one of Smokey Bear's black-and-whites.
Park employees learned it almost as soon as they learned where to pin their name tags and the appropriate way to wear the flat-brimmed Smokey Bear hat.
He wore a green robe slashed with brown and the Smokey Bear hat, the uniform of the Central Park ranger.