The Vikings of Berk sleep just like everyone else. And what better to sleep on than Berkian beds.
Berkian beds are traditionally made of wood, with decorative carvings on the frame as well as on the head and foot boards. Carvings on the headboard are often also dyed another color, giving them an element of beauty. They also usually have four posts, the two at the head with an animal, usually a dragon, carved on the top.
Being Vikings, they're tough, and must not need much in the way of comfort, because they always sleep directly on the wood planks, without even an animal pelt for cushion. A small sack, likely stuffed with straw, is used as the pillow. And a single quilt is usually their only covering. Given they usually sleep in their clothes, including boots, they must not need much warmth, either.