I just searched this and there some You Tube video's on training your dog how to ride a quad (one is beagles). Appears you have to start slowly with the engine off, no movement and then have them get used to the noise prior to any movement. Then start them on it very slow speeds and level ground. There are also harnesses depending on the type of seating you have. In the end it's going to depend on how skittish your beagles are and how much time you are willing to invest in training them. My beagle would have been way to frightened of this - we had a long introduction to everything, she started out being afraid of grocery bags and anything delivered in a box! She also tried to dig her way through the floor of the car; she was much better crated than on a seat.