1. Don't forget that Finland was part of Russia and had army and army supplies. They were happy to be part of the Russian Empire, but didn't want to join the new Communist USSR.
2. After WW1 they bought lots of old stock Mosins from around the world, e.g. Poland (large amounts, who was also part of Russian Empire + had lots of fighting during WW1), Germany, Austria, US (as the majority of the shipment never made it before 1917 Russian civil war).
Interesting fact, Finland never produced a single receiver for its Mosins.
3. The number of captured rifles was not that great. Even in the Winter war (despite all propaganda on this side for the last 75 years), the real fact is that Finns lost it.