I recently bought a Mosin Nagant, and while there's no record of what rifles saw combat, I was able to trace back the serial and manufacturer to find out that my rifle was shipped to Russia from the US in 1937, so it more than likely was given to a soldier at least.
I wondered about all the hands this weapon must have passed through, and all the nicks and scratches in the wood and metal which got me wondering. What happened to all of the other WWII weapons? I know many of the German guns were melted down for the metal, and of course you find ruins on beaches or in the woods, but for the majority of it where did it go? There must have been 10s of thousands of Thompson Machine guns, Garands, Carbines, tanks, etc. Did the US ship back all of their equipment at the end of the war, or were / are there piles of american weapons somewhere in Europe?
I know Lord of War is a fictional movie, but was there a large underground gun trade / smuggling operations after the war like are depicted with current US weapons after combat situations?
I was able to trace back the serial and manufacturer to find out that my rifle was shipped to Russia from the US in 1937
Is that a typo? Because while Remington made a few hundred thousand Mosin rifles in the US during World War I, I was under the impression that none were shipped to the Soviets post-October Revolution, so I certainly find it strange that they would have been exported as late as 1937. I'm curious what source you found that posits shipments happening in 1937.
Annnnnyways though, to answer your actual question. In the case of the Soviet Union, most of the arms were returned to the arsenal to be evaluated for condition. They would be refurbished, and those that weren't needed for issuance were crated. Some of the arms would find their ways to various countries or groups backed by the Soviets, while many of them were simply put into storage for World War III. The fall of the Soviet Union - as well as changes to laws governing the import of firearms into the US - saw these crates of Mosins start to be imported to the United States in the 1990s at bargain barrel prices, which is why everyone seems to own one, although fears that the supplies of 91/30s have seen the overall prices rise some over the past 20 years.
In the case of German arms, some stuff was taken home as war trophies (this applies to Japanese arms as well). I've written a post before about this but the gist is that it was seen as important to morale to allow soldiers to do so, so as long as you had permission and followed the guidelines, it was quite easy. As you state, much of it was simply destroyed. However weaponry also ended up all over the place. Israel is the most famous example, buying a number of Mausers from Czechoslovakia at around the time of their declaration of independence, so Israeli Mausers - which have both the Nazi proofmarks and the Israeli proofmarks - are quite sought after by collectors. The Soviets also did the same thing with the Mausers that they did with their Mosins, crating them for a "just in case" scenario. Like with the Mosins, these ended up on the American market in the 1990s, where they are generally called "Russian captures".
With the Americans, production of the M1 ended with the war, and like with the Soviets, hundreds of thousands of the rifles were refurbished, although they didn't end up in underground mines waiting for the apocalypse as far as I'm aware. Many were sent as aid to other countries who were in the Western camp. Eventually, they started being sold off by the Civilian Marksmanship Program. Not being well versed in regards to the American program though, someone else would have to expand beyond that.
In the case of other equipment besides the firearms, a lot of it went to various allies. The many French soldiers were fighting in US military surplus in Indochina. American and German tanks did battle in the middle east, between Israel and her Arab neighbors. Excess naval ships were sent off to countries who didn't have the industry for it themselves.