I don't know how rare they actually are, but I've never seen one with my own eyes. I've seen them on the internet, but there aren't any currently for sale on GunBroker or GunsAmerica. My hunch is that they are pretty rare.
My dad told me a little about them from what he learned as a Marine Corps armorer at Quantico in the late Fifties. He had access to Warsaw Pact small arms, and he told me that the Czechs reworked some of their Mosin rifles in the late Thirties as carbines. That's about all he told me, and he isn't around to ask anymore.
I did "Saturday afternoon" internet research on them a couple of years ago, but most of the forum posts and internet articles seemed to be very wrong about the rifle's origins. Most of the articles I found assumed that the rifles were created as a response to the Soviet Union taking over Czechoslovakia in 1948, and the creation of the Warsaw Pact as a response to the creation of NATO. That is a bad assumption. The Czechs reworked these Mosin Model 1891 rifles in the late 1930's, long before the Communist takeover and long before the creation of the Warsaw Pact. It's an understandable mistake, because some history was forgotten....
Before there was a Czechoslovakia, Bohemia, Moravia, Slovakia, Silesia, and many other ancient kingdoms were dominated by the Austro-Hungarian Empire, and they longed to be free. Peoples of these nations were conscripted into the Austro-Hungarian army, forced to fight in World War 1 for a conquering empire they did not support. Thousands of Czechs, Slovaks, Silesians, Ruthenians, Slovenians, Italians, and others who were sent to fight Russia deserted to the Russians to weaken Austria-Hungary and end their domination. In a few instances, entire regiments marched across the front lines under white flags and surrendered en masse to the Russian army. From their POW camps in Siberia, they then petitioned the Russian government to join the Russian army to fight the Austrians to throw off their oppression. In late 1916 the Tsar agreed to the idea, and by the March Revolution in 1917 there were Czech Legions with more than 30,000 soldiers in the Russian army.
The soldiers in the Czech Legions were re-equipped with standard Russian uniforms and equipment, including Mosin rifles, artillery, machine guns, and a unique helmet that had the coats of arms of Bohemia, Moravia, Slovakia, and Silesia instead of the Romanov eagle. But the story gets even better....
After the Tsar abdicated, a provisional government took over and continued the war against Germany, Austria-Hungary, and Turkey. The Czech Legions continued to attract volunteers from the POW camps throughout Siberia, and continued to grow even as the Russian armies fell apart in the field. The Bolsheviks took power in November of 1917 (October in the Julian calendar still used in Russia), and they signed the Brest-Litovsk Treaty that took Russia out of the war in March of 1918.
The Czecho-Slovak Legions, as they were called, still wanted to fight for the liberation of their homelands from Austro-Hungarian domination, so they arranged with Lenin himself to be transported out of Russia fully armed via the Siberian Railway through Vladivostok, through the US, to the battlefields of France. The Legions began their transport in April 1918, but even before the first trainloads reached Vladivostok Trotsky decided that the Czech Legions would make an excellent basis for a new Red Army (since the Russian armies had all mutinied and walked home after the October Revolution), so he ordered that their transport be hindered, and that the Czechs be disarmed. There is debate as to whether the Germans also lobbied to have the Czecho-Slovak Legions arrested and sent back to the Austrians for execution, but it is plausible.
The upshot is that the Czechs got strung out along 6000 miles of railroad, separated into small groups, and then the Red Guards started shooting on the trains. Then the almost entirely unarmed Czechs fought back and quickly managed to capture almost the entire length of the Siberian Railroad from the Volga River to Vladivostok between May and July of 1918. The Czechs then recaptured tens of thousands of German, Austrian, and Hungarian POW's who were being transported back to their homelands from POW camps in Siberia as part of the Brest-Litovsk Treaty as a service to the Allies. This prevented Germany and Austria-Hungary from redeploying these "fresh troops" against the Allies, which might have tipped the balance of power against France, Britain, Italy, and the US. By doing this, the Czecho-Slovak Legions ensured that when Germany, Austria-Hungary, and Turkey surrendered in November, 1918 that the victorious allies guaranteed that their homelands would be free of Austria and Hungary as the newly created countries of Czechoslovakia, Poland, and Yugoslavia.
Oh, by the time that the war ended, the Czecho-Slovak Legions had grown to between 60,000-100,000 soldiers. Some of those men were from countries other than Czechoslovakia, like Italy, Yugoslavia, Romania, elsewhere. Unfortunately, the war didn't end for the Czecho-Slovak Legions because the Bolsheviks were still at war against them, trying to recapture Siberia. When the Czechs finally made a deal with the Bolsheviks (they traded the Tsar's gold reserves and the leader of the Siberian revolt for safe passage) they eventually transported more than 60,000 troops by ship back to Europe. Those troops left fully armed with Mosin rifles. Several thousand other troops elected to walk home in small groups instead, and they left fully armed with Mosin rifles too.
The "First Republic" of Czechoslovakia reworked many of those rifles into the Mosin 91/38 carbines for their own uses in the late 1930's. That's why the 91/38 rifles have production stamps and proof marks from imperial Russia before WW1. The Czechs also had a vast reserve of Mauser rifles from the Austrian army regiments that Czechs belonged to, and the Czech army used mostly Austrian army equipment all through the Twenties and Thirties, such as the "storm trooper" helmet that the Germans and Austrians adopted in 1917 that eventually morphed into the German helmets of WW2. The Czech front-line troops were equipped with CZ vz. 24 rifles, but reserve units and training units were probably equipped with Mosin rifles, much like US National Guard units had Model 1917 "Enfield" rifles up to the beginning of WW2.
I don't know how many rifles were converted to 91/38 carbines. I'll probably hunt around the internet in the next few days to see if I can find a Czech language article with an estimate of numbers. I have a hunch that there weren't many to start with. Imagine if 50,000 legionnaires took their Mosin rifles home, then only some of those were converted into carbines... well, there wouldn't have been more carbines when they were done than rifles when they started. CZ had machine tools to make new "Mauser K98" rifles, but no machine tools to make new Mosins. It would have been a stopgap, probably. It's just speculation on my part....
So, if you can find a Mosin 91/38, you'll have a piece of forgotten history that you can keep alive. Good luck finding one. Show us pictures if you do.
Scott