Northern European ships during the Viking-Age did not have roofs. A roof would block visibility between the skipper at the stern and anything happening at the bow of the ship. A roof would also get in the way of rigging and handling the sails.

Exposure was, of course, an issue, which is why most voyages likely kept close to shore, and we have no records (at least none come to mind) of long voyages during the winter. When boats put into shore, their crews likely set up camp to give them some relief from the sea and the sun. At Ribe in Denmark, for example, traders set up seasonal tent cities, most likely during the summer months. Sagas tell us that transient populations like merchants would often seek out a friendly patron to host them in their hall over the winter.

We've got a few great examples of Viking Age ships which have survived archaeologically. I recently wrote up a description of what life was like on a longship. Give it a read and let me know if you have any questions. There's also a few links that might be worth following if you'd like to learn more. In particular, I'd point you to the numerous videos that have been made documenting replica voyages, as well as the voyage records of the Viking Ship Museum in Roskilde, DK.