befog

To envelop in fog or smoke.

Clouds of the most expensive incense befog the chancel […]

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.

“[…] He’s been blarneying you. You’ve let his plausible tongue and handsome face befog you.”

To obscure, make less clear (a subject, issue, etc.).

How they had managed to befog the subject! What elaborate show-structures they had built up, with no result but to obscure the horizon!

There is only one way to understand syphilis, and that is to give it impartial, discriminating discussion as an issue which concerns the general health. To color it up and hang it in a gallery of horrors, or to befog it with verbal turnings and twistings, are equally serious mistakes.