The seminal article by Frank explains as the diffusion of the idea of a viking with the horned helmet as following:

• The direct ancestor/ culprit of the idea was prof. Carl Emil Doepler, a costume designer for the Wagnerian opera, Der Ring des Nibelungen, that was performed in Bayreuth in 1876.
• After this Doepler's costume in the opera, the horned helm got popular first in English and German children's as well as popular history books within the last decades in the 19th century, but the Scandinavians was generally not so eager to accept this representation of the Vikings at least by the beginning of the 20th century.

Frank identifies one further ultimate provenance of this horned helmet with the early modern commentary of the printed edition of Tacitus' Germania, written in the 1st century CE: Erroneously based on a description of [one of] the diverse helms of the Celts, and Cimbri in ancient Denmark, some humanists had considered the possibility that various peoples in ancient Northern Europe, not only the Celts and Cimbri, might in fact put horned helmets on their heads at least since the 17th century. I wish to emphasize 'ancient', not the Viking Age, though.

Doepler adopted the horned helm from Tacitus' commentary into the costumes of Wagner Opera, then this new trend of costume was further 'imported' into the Vikings.

Reference(s):

• Frank, Roberta. 'The Invention of the Viking Horned Helmet'. In: International Scandinavian and Medieval Studies in Memory of Gerd Wolfgang Weber, pp. 199-208. Trieste, 2000.

The imagery of the "horned Viking" is the result almost entirely of one man: Carl Emil Doepler, the costume designer for opera auteur and horrible human being Richard Wagner. In the premiere performance of Die Ring des Nibelungen, the antagonist, Hunding, and his followers wear horned helmets, while the heroic, if uncivilized, Nibelungen and Siegfried wear shining chainmail or very little at all. Now, Hunding wasn't a Viking - the Æsir appear in the opera and Odin and the Valkyrjur wear helmets with wings on them. However, the horned helmet is equated to brutality and being an "enemy" in the opera.

Wagner's shows were a ridiculous mega-hit, and audiences quickly appropriated Hunding's horned helmet to the Vikings themselves, as the ultraviolent ravagers described in the medieval annals. Later performances of Wagner's operas in the early 20th century show horned helmets all over the place, and by the emergence of medievalist pulp, such as Howard's Conan the Barbarian, the association is firmly cemented of the horned Viking.