The name was coined as its original describer concluded it was special because the nose-horn was not a separate bone, however further analysis revealed this was based on a misunderstanding.

[1] It lived during the latest Campanian/earliest Maastrichtian stage of the Late Cretaceous, predating its famous relative Triceratops by a few million years, although it was contemporary with Anchiceratops.

[1] Described by William Arthur Parks in 1925, Arrhinoceratops is known from a partially crushed, slightly distorted skull which lacked the lower jaws.

The remains were collected from the Neill's Ranch site, along the Red Deer River in Alberta by a 1923 expedition from the University of Toronto.

The generic name is derived from Greek α~, "without", ῥίς, rhis, "nose", κέρας, keras, "horn", and ὤψ, ops, "face" as Parks had established that no separate nose-horn was present.

In 1981 Helen Tyson in a revision of the genus, provisionally referred specimen ROM 1439,[6] but in 2007 Andrew Farke moved this to Torosaurus.

The most notable of these was that the very trait the genus was named after, the lack of a separate ossification or os epinasale for the nose-horn, is in fact normal for the ceratopsids, in which group this horn is an outgrowth of the nasal bone, not a distinct element.

Other incorrect observations by Parks included the conclusion that the os rostrale, the bone core of the upper beak, directly touched the nasals instead of being separated from them by the premaxillae; a presumed anterior process of the jugal touching the premaxilla; and thinking that the interparietal bar of the frill presented a separate skeletal element, an os interparietale.

[6] Arrhinoceratops was by Parks placed within the Ceratopsia (this name is Ancient Greek for "horned faces"), a group of herbivorous dinosaurs with parrot-like beaks which thrived in North America and Asia during the Cretaceous Period, which ended roughly 66 million years ago.