I have friends who sailed in Lake Ontario with a 13 year old Great Dane named "Wilma". But the boat was steel, and she looked half-dead already, the poor old dear. She needed assistance with the companionway, but mostly stayed curled up (ok, a big curl) in the center cockpit.
They took her out in pretty tame weather, but she went with them on longer cruises, too. Now they have little 20 lb. poodle crosses that are more suitable.
But that's Lake Ontario. I am pretty sure they wouldn't consider going offshore or even in situations where there were swells of any size, with their dogs.