We once took 4 dogs (ranging from a yorkie to a German Shepherd) to Morfa Lodge at Dinas Dinlle near Caernarfon. They dont usually allow that many but I rang them first and explained that they were all well behaved and would cause no trouble and they agreed because it was a quiet time and the site was fairly empty. If you try the smaller privately owned sites you often find they will agree to bend the rules. This site may not suit everyone but we liked it. It has a small airfield next door which is busy with light aircraft at the weekend and the other drawback is it can get boggy, but there is a nice beach at Dinas Dinlle and it is close to Caernarfon and all the attractions of that area. There is a pool on the site and a shop etc. Check www.ukcampsites.co.uk for site reviews.
Zarndra - We have 2 dogs which travel to every site with us. We are Caravan Club members and always check if dogs are allowed at sites by looking in the members handbook, the details also tell you if thee is a dog walking place on site or nearby. There are some (but not that many) sites which don't allow dogs.