You are correct that a dolphin's blowhole is not its nose in the traditional sense, but it does serve a similar function in that it is used for breathing. However, the reason a dolphin would play a trumpet with its blowhole rather than its mouth has more to do with the anatomy of its airway than with the function of the blowhole itself.

Dolphins are mammals and breathe air into their lungs just like humans do. However, unlike humans, dolphins do not have a direct connection between their mouths and their lungs. Instead, their airway consists of a long, narrow passageway that leads from the blowhole on the top of their heads down to their lungs. This passageway is called the pharynx, and it is not connected to the mouth or the digestive tract.

This unique anatomy means that dolphins are not able to inhale or exhale through their mouths, and they cannot control the airflow through their mouths in the same way that humans can. Instead, they use their blowhole for breathing, and they have excellent control over the muscles surrounding the pharynx, which allows them to produce a variety of sounds for communication.

So, if a dolphin were to attempt to play a trumpet (or any other wind instrument), it would have to use its blowhole rather than its mouth because that is the only way it is physically capable of controlling the airflow to produce sound. The dolphin would essentially be using the trumpet as an extension of its own respiratory system, blowing air through the instrument with its blowhole and using its pharyngeal muscles to modulate the airflow and create musical notes.

In conclusion, while a dolphin's blowhole may not be a "nose" in the traditional sense, it is the functional equivalent when it comes to breathing and sound production. And due to the unique anatomy of a dolphin's airway, it would indeed use its blowhole, rather than its mouth, to play a trumpet.