In the history of Halloween it appears American dogs began dressing up and going trick or treating about the same time the children did.
Some historians believe that most of the traditions of Halloween date back to around 800 BC with the Celtic people. The Celtics celebrated their New Year on November 1st, when the weather was turning colder and the last crop was harvested. This was a big turning point for them which they believed was a magical time - when the dead would roam the earth. So when one year turned to the next, the young men would dress up in white costumes and black masks to protect themselves from evil spirits - this was to help fool evil spirits into thinking they were an evil spirit as well.
Trick or treating, or guising (from disguising), traditions began in the Middle Ages. During Hallowmas (Nov 1), children would dress up like a spiritual being and go door to door to beg for money or food in exchange for songs and prayers, often said on behalf of the dead.
The practice of guising came to the US in the late 19th or early 20th century. The first documented reference is in 1911. It was in the 1920s and 1930s that the practice of trick or treating replaced guising. The earliest known document with the word trick or treat is a news article dated November 4, 1927. The practice first started in the western part of the country and slowly made its way across the country. During WWII, it took a brief respite because of sugar rations, but came back strong afterwards. Today, Halloween is one of the most commercially successful holidays in the US.
I don't know when families started to dress up their dogs to take trick or treating, but by the appearance of the first photo at the top of the page I would say it was about the time when Halloween was making its way across the country.
