Surfing on Ice

Well, not really Ice. But this is 6°water, 7°C air and a fresh wind and there are surfers in the water on a crappy windswell beachbreak. The coldest I have ever done was 10°, and that was already very very cold.

How do you stay warm? What kind of suit, shoes and gloves do you need? Do you need a suit with an integrated hood?
But even with a thick suit, isn't the cold wind and water in your face making you cold?
How do you stay warm? What kind of suit, shoes and gloves do you need? Do you need a suit with an integrated hood?
But even with a thick suit, isn't the cold wind and water in your face making you cold?