The birds' shiny feathers are coated in natural oils that keep them warm and waterproof in the icy waters. The crude oil from the spill destroys the penguins' natural oils. When this happens, the birds cannot protect themselves from the cold.
To make matters worse, penguins preen - they clean and smooth their feathers using their beaks. If a penguin preens after an oil spill, it will swallow poisonous oil, and probably die.
The wool sweaters keep in the penguins' body heat, and prevent them from being poisoned by the oils.