Dogs are a stationary obstacle in Thief much like birds. Nearly all dogs are kept within cages. If Garrett gets close within a dog's field of view, it will start to sniff him, raising awareness. If Garrett doesn't get out of sight, it will start barking, alerting anyone nearby. This makes them a slightly greater threat than birds and they are often found in places to block certain paths. A dog that starts barking counts as being detected.
Only in one action sequence are they seen chasing Garrett.