Actually the "pouf-pouf" haircuts were used for poodles when they were used for hunting, especially as water retrievers.
They had too much natural hair, which would get waterlogged and drag them under when they went into water to retrieve the birds brought down by the hunters.
But cutting all the fur off made it too cold for the dogs and they would develop arthritis at an early age. So the hunters began leaving the fur around the front shoulders to keep them warm to ward off the arthritis.
The facial hair was cut very short to it did not cover they eyes or get in the way of their mouth, used to retrieve ducks and other game.
Thanks for the added info - a day I haven't learned something is a day I've wasted. (Not original, but I don't know who said it first.) That doesn't explain the cuff patches, which would seem to hinder swimming. Maybe those were later additions for dog shows.