What term describes a type of pony that does not have a specific breed registry but is recorded by the USEF?

The term that describes a type of pony that does not have a specific breed registry but is recognized by the United States Equestrian Federation (USEF) is indeed Hunter Pony. Hunter Ponies are categorized based on their performance abilities and suitability for hunter events rather than a formal breed classification. They can come from various breeds and are judged on their ability to navigate jumps and perform in a show ring setting, which allows for a diverse range of ponies to compete under this classification.

In contrast, the other options listed are recognized breed registries with specific breed characteristics and standards. The Friesian is a specific breed known for its distinctive black coat and elegant movement. The Oldenburg is a warmblood breed often recognized for its athleticism and performance in various equestrian disciplines. A mule is a hybrid animal (the offspring of a male donkey and a female horse) and does not fit the definition of a pony nor does it have a corresponding breed registry for performance similar to that of Hunter Ponies.