Sausage in some manner has been around for a very very long time. Where exactly a sausage turns into a hot dog is certainly up for debate. Frankfurt claims to be the originator, though some state it was a butcher from Coburg Germany who created the sausage and eventually brought it to Frankfurt. Vienna also has a claim to the first Hot dog.

Many hot dog historians believe that the American style dog is actually an amalgamation of many cultures' sausages styles that eventually morphed into the cylindrical meat that we know and love.

But of course a sausage alone does not a sandwich make.

A sandwich is defined as:

"a : two or more slices of bread or a split roll having a filling in between

b : one slice of bread covered with food"

This can, and jas been interpreted broadly amd narrowly depending on the source. Is a taco or burrito a sandwich as well?

It is believed that the first true hot dog (sausage in the split roll), emerged in New York sometime in the middle of the 19th century.

At this time the tubular to-go treat was sometimes called a Coney island sandwich or a Frankfurter sandwich. Though some papers have since published corrections to these stories published over 100 years ago.

So to the heart of your question, depending on the source, the American style hot dog has been called and considered a sandwich.

The term hot dog however followed later, some believe that a cartoon penned around 1901 was responsible for spreading the term, but there is no evidence to support this. Some wiener historians point to mentions of a "hot dog as in campus magazines from yale as a source for the popularization of the word around 1894.

But what do the professionals say?

The esteemed National Hot Dog and Sausage Council (NHDSC), the protector of hot dog purity in the United States has declared that no, a hot dog is not a sandwich.

Sources: Mentions as a sandwich Definition Council declaration General hot dog info