Some guidebooks say that there are more donkeys in Santoini than inhabitants.:) In fact, you will probably see many donkeys and mules during your visit to Oia. Ddonkeys and mules are part of the native charm of the island and can be loads of fun. There are still places in Oia where you can get only by donkey as there is no road. Than the best way is to take a donkey taxi. ;)
Cats and dogs are everywhere. They are lying on the pedastrian paths. Dogs prefer lying in the middle of the path what can be anoying becasue when there is a big crowd it makes the situation complicated.
As most hotels are on caldera it is easy for acts to move. It may be nit that nice when you are sitting on a hotel's tarrace and cats are coming and witing until you give them sometihing to eat. The more guests feed cats the more often they come. Hehe.