google Welsh Sport Horses - Anne & Jane Roberts. They run a stud and have a holiday cottage for let. I know they are basically right on the beach and ride along it freely.
Anglesey Riding Centre at Tal Y Foel located on Menai straits does holiday livery. They may have a b&b too. If not then there will be plenty close by. Good riding on beach. Porth Y Post Stables in Trearddur Bay also does holiday livery. Hacking not as good although you can ride on Trearddur Bay beach. Lots of accom in and around Trearddur Bay. Ask Sylvia who owns yard. If you want to do beach riding then south and east coast are best as north and west coast have a lot of cliffs. Cymyran, Rhosneigr, and Newborough are excellent beaches for riding on. If you speak to the Cymyran Hotel then they have some land that they might let you keep your horse on for a holiday. Speak to Pryd who owns the hotel.