No source shows that Churchill said it. The historian Richard M. Langworth lists it under “Red Herrings: False Attributions” in Churchill by Himself, the fullest collection of Churchill's quotations. The earliest strong match Quote Investigator found was spoken in 1919 by Bertram Carr, Mayor of Carlisle, and halves of the saying were in print earlier.
What it means
Two people can face the same situation and see opposite things: one sees the snags in every chance, the other the chance in every snag. It is a case for the second habit of mind.
Where it comes from
Addressing the Co-operative Congress in Carlisle in 1919, Carr spoke of viewing old problems “in the spirit of the optimist to whom every difficulty is an opportunity, and not as the pessimist, to whom every opportunity presents some difficulty.” Quote Investigator treats Carr's credit as tentative, because pieces of the saying were already around: in 1903 one writer described a pessimist who “can interpose a difficulty in every opportunity”, and another advised: “Suggest to yourself an opportunity in every difficulty.”
By the 1920s the paired form was a newspaper filler, unattributed or credited to various speakers, including John D. Rockefeller (1925) and the minister L. P. Jacks (1929). Churchill did once tell a joke about optimists and pessimists, in a 1938 essay, but it was a different joke.