The word for hot-dog in Italian is exactly the same as it is in English. Being of American origin, the hot-dog retains its language of origin, although an Italian speaker would probably drop the 'h' sound as it is always silent in Italian. If referring to the actual sausage used in a hot-dog, Italians would be more likely to use the words Frankfurter or Wüster.
There are a variety of different reasons why the Italian language might absorb foreign words into its lexicon. In the case of the word 'hot-dog' it is because there was not a previous word in place for it. Other times it is simply easier or shorter to use a foreign word in place of the original word or phrase. For example, an Italian suffering from lo stress (or la tensione emotiva) after a hard day in the office, might be looking forward to il weekend (or la fine settimana).
Another reasons that Italian adopts English words is because they are considered chic or trendy, as seen by the abundant use of the word sexy.
