My last mutt went everywhere with us. In bad weather he was jammed in at the front of the seat between the console where was was quite happy. However in anything bar reaaly bad weather (and remember we didn't usually want to be out in this either!) he was very happy hanging over the side biting the spray.
The new one has a new lifejacket but hasn't been out as yet as I rebuild the outboard and refurbish the rib but we, and the dog, generally preferred to be out on the boat than left in the house.
Do the pics and video look as if he didn't want to be there?