Long title, I know, and it may not explain my question the best.
So, for a while Fascism existed as a kind of legitimate ideology; at least in the sense that it did have a major impact in multiple countries and gave birth to parties striving to put fascist ideals into practice. After the horrors it unleashed in WWII for the most part Fascism as an ideology kind of just... well, died off. There exists far-right nationalist groups, of course, but as any kind of "legitimate" ideology it has been thoroughly discredit by the wider world and ultimately rejected.
Even today many "fascist" groups generally place an emphasis on racial politics and nativism rather than the other aspects of Fascism such as national fraternity, radical change, opposition to Marxism, so on.
The Socialist movement, comparatively, has managed to survive the fall of the Soviet Union, even if it's been bloodied. You still have some openly Socialist politicians making waves with people, some nations openly aligning themselves based off of "Socialist" economic models, heck you even have a few very light "Socialist" works and views gaining popularity.
What I want to ask is why, by comparison, does it seem like Fascism just up and died as any significant ideology after WWII when Socialism is doing comparatively alright? Both sides horrifying acts committed in their name and both sides suffered a large blow when the major nations pushing "Socialism/Fascism" up and died. Can any Historians point to an exact time where Fascism as an ideology just up and dropped out of relevance? Did any kind of openly Fascist groups anywhere see a light revival during the cold war because of their opposition to Marxism?
I'm intrigued.
I can't accept a few premises in this question. Firstly, fascist governments, or coalition government partners, have existed in many countries since WW2, including European ones. Secondly, the collapse of a socialist system in a country (your mentioning of the USSR) is as likely to mark the end of socialism as the collapse of a capitalist one in another country (Greece, say). Thirdly, horrors are not something that ensures the death of any system. For example capitalism is alive and well despite its death count.
After the horrors it unleashed in WWII for the most part Fascism as an ideology kind of just... well, died off.
This is just not true. After WW2 fascist and fasc-ish governments survived and thrived in Spain, Portugal, and Argentina. The Christian militias of the Lebanese civil war(1975-90) were originally based on the Hitler Youth(making their alliance with Israel unusually perverse) and, of course, there's also the Golden Dawn rising in Greece.
Why would the collapse of Marxism-Leninism be expected to discredit parties that strongly opposed Marxism-Leninism? The Communist Party in Germany, for instance, regarded the Social Democrats as their greatest foe for most of their history, and the Social Democrats in turn repressed them violently as a threat to the Constitutional order.
Those of the "socialist" parties today that are actually relevant, politically, are largely Social Democratic or Labour parties that can trace their roots to the Second International. These parties opposed and competed against the Comintern since its foundation.
Those "socialist" parties that actually have their roots in the pre-1989 Comintern, like Germany's Die Linke or France's Communist party, are much smaller than the anti-Leninist "socialist" parties, and generally quite marginal.
This smells like a loaded question, but essentially, as others have pointed out, the fundamental premises of your question are deeply flawed. There have been a lot of very sharp differences of opinion among Marxist political groups. Marxists have long viewed fascists as their ultimate enemies, but many times they have hated each other all the more bitterly, for a variety of reasons.
This is a very poor analogy, but consider the way Western civilization and Islam, broadly, are seen as being in conflict today, by many people. Many would disagree that they are in conflict, and then many would also point out that Sunnis and Shi'ites commit extraordinary acts of violence against one another, even while they stand opposed to Western interests.
The world is a much more complex place than you seem to suppose, based on how you asked this question.