Wiktionary
a. (context of a person , or of an argument or thought process English) illogical, irrational.
WordNet
Usage examples of "woolly-headed".
While I was busy arguing and persuading the woolly-headed cannibals to come and labor on the Queensland plantations Otoo kept watch.
They had turned his woolly-headed romantic notion of a single duel into a death-trap.
She had to make and receive at least fourteen presents,—to make fourteen solemn promises of writing every week: “Send my letters under cover to my grandpapa, the Earl of Dexter,” said Miss Saltire (who, by the way, was rather shabby): “Never mind the postage, but write every day, you dear darling,” said the impetuous and woolly-headed, but generous and affectionate Miss Swartz.
I don't know what I had expected-one of your woolly-headed darkies, I suppose, massa-ing everyone, and pathetically grateful that someone was going to risk his neck to help him to freedom.
Now, you may call that woolly-headed idealism if you like - but I call it hard-headed human compassion.