The horned helmet thing specifically seems to come from the hugely popular Der Ring Das Nibelungen, a cycle of four operas by Richard Wagner. It's seen as one of the crowning achievements of Romantic opera, in large part because it gave us the "kill the wabbit" song. (OK, it's actually because of its scale, the richness of its plot and mythology, the musical themes and motifs that are woven throughout its 15 hour runtime, and the incredible spectacle of seeing it staged.)

Wagner wrote the libretto (words/plot) himself, based on various Germanic and Norse legends. Most prominently, it's based off of the Nibelungenlied, which concerns the hero Siegfried and his exploits. Siegfried is the main hero in Wagner's Ring as well, but Wagner drew from other stories and added his own elements. The plot centers around a ring, forged by a dwarf, that gives the bearer immense power, and the struggles between gods, men, and other beings to control that ring. If that sounds familiar, it's because JRR Tolkien and Wagner drew inspiration from many similar sources and traditions, although the exact amount of influence Wagner's opera may have exerted on Tolkien is disputed.

As I mentioned earlier, Wagner's Ring is generally considered one of the greatest works in all of opera. Love it or hate it (and there are plenty on both sides!), it is an incredible undertaking. Everything about it is massive and complex. Wagner believed in opera as a great melding of multiple art forms, from drama to visual arts to music. His operas are [epic in scale], visually striking, extremely dramatic, and just generally written to invoke a sense of awe and a deep engagement from the audience. Wagner also preferred to see his creations as single works, made to be taken as a whole. He had a specific vision for how everything fit together, and saw anything that deviated from that vision as detrimental to his grand artistic plan. Wagner went so far as to build his own theatre and create a festival devoted to performing his operas exactly as he envisioned them in Bayreuth, a Bavarian city. Wagner had and has a very dedicated fan base, and his singular style and vision is the main reason why.

The first edition of the Bayreuth Festival, in 1876, featured the first performances of the Ring cycle in its entirety. The costumes were designed by an artist named Carl Emil Doepler. They are remarkable for being both wonderfully evocative and wildly inaccurate. And if you take a look at the drawings here, you'll notice that some of the warriors are wearing horned helmets. The massive popularity of Wagner's Ring cycle launched that particular look into popular consciousness. German nationalism was on the rise in the late 19th century, and the legends of the ancient Germanic and Norse peoples were very popular subjects in art. These legends were also a way of asserting a proud and ancient and (most importantly) indigenous mythology separate from the classical Greek and Roman mythology that enjoyed prestige in Europe. It's a bit of the old "see, we've got great legends and heroes and gods, too! And hey, ours have some pretty awesome headgear!"

As far as we know, Germanic warriors wearing horned helmets thing became engrained in popular culture through this production of the Ring and the many subsequent productions that used similar costume designs. As the Vikings became the most commonly known archetype of Germanic warrior, they became most strongly associated with the horned helmet trope. The Ring is also where the whole "fat lady with a spear and a horned helmet singing opera" stereotype comes from. It's based on the role of Brünnhilde, a major character in the Ring. She often carries a spear, often wears a helmet, and the singers who sing the role come in all shapes and sizes, including many who are on the larger side. Her long aria towards the end of the final opera of the cycle is where the phrase "it ain't over till the fat lady sings" comes from.