1953, Jean Stafford, “Cops and Robbers” (original title: “The Shorn Lamb”) in The Collected Stories of Jean Stafford, New York: Dutton, 1984, p. 432,
Sad, in her covert, Hannah saw that her mother was now sitting straight against the headboard and was smoking a cigarette in long, meditative puffs; the smoke befogged her frowning forehead.
To confuse, mystify (a person); to make less acute or perceptive, to cloud (a person’s faculties).
1871, Carl Schurz, Speech in the U.S. Senate, 27 January, 1871, in Frederic Bancroft (ed.), Speeches, Correspondence and Political Papers of Carl Schurz, New York: Putnam, 1913, Volume II, p. 151,
The voice of interested sycophancy is apt to fill their ears and to befog their judgment.
To obscure, make less clear (a subject, issue, etc.).