Allow me to make a small contribution to this, please.
Incidentally, in the latest issue of the "Kaliberi" weapons journal, there was an article about the model 1895 in which I take a keen interest.

About the 9,3mm caliber:
In the 50's and after WWII, civilians were not allowed to own rifles in military caliber.
The most common weapons probably were the Mosin-Nagant and its derivatives, and certainly the Win was never a rarity. Some confusion may have been caused by the Finnish nomination "Vintovka" to describe various weapons especially around the time of Finland gaining its independence in 1917.
However, the most common caliber was the 7,62x53R (I'll use the Finnish nomination, OK?) which was the military round of the Russian army and which also became the Finnish standard until effectively 1962 when the m/62 assault rifle (Valmet) in 7,62x39 was introduced. Even after this, the old rimmed round has seen service and still sees today in both sniper rifles (rifle m/85) and the "new" light machine gun PKM which replaced the old Finnish made m/62 (incidentally the same model year designation as the assault rifle) in 7,62x39. The newer sniper rifles are chambered in .308 Win and .338 Lapua Magnum, and also we have the .50 BMG but it's rather a rarity.
Also after the war the law dictated that for moose the minimum caliber was 8mm, ref. 9,3x57's "Moose law round" nomination.
The easiest way to obtain decent hunting rifles in a poor country was to convert the existing rifles to shoot a larger-diameter bullet. The 8mm and 9,3mm were chosen due to good availability: the 8,2mm is .323" in diameter, i.e. the same as the German 8mm Mauser, and the 9,3mm is also a common enough German caliber so the choices were rather logical.
I have also heard of, although never seen, 7mm and 6,5mm conversions of the same.
The topic came up in another thread, and then I learned that the Russian 9x53R is NOT the same as the Finnish one. I believe the Russian one in practice runs on lower pressures although the CIP max. is the same for both. Looking at the cartridge drawings the differences are minimal. The principal difference is the overall length which for the Finnish variant is 76mm and for the Russian 67mm.
The bullet diameters are quoted as 9,3mm and 9,27mm, respectively.
The current official CIP pressure is 3400 bar (PTMax) for both, as well as for the 8,2mm.
For comparison, the 7,62 PTMax is 3900 bar - whence the difference is beyond me.
The CIP table does not quote pressures for the smaller bullets suggesting they are rare, indeed.
The 9,3mm variant was as far as I know never as popular as the 8,2mm - probably due to the bullet been seen as "too large" (?) and also the 8mm doing a dandy job. The 9,3mm has always had a reputation of hefty recoil. I doubt if many have ever actually fired one; my guess would be the impression of the 9,3mm as "a large caliber". One would also assume bullet availability has played a role in the 8,2mm becoming more popular.
The 9,3mm was typically loaded with the 255grs bullet which is light for the caliber, and at low velocities. The case capacity of the x53R v. the German 9,3x57R is negligeble so most likely the same load data could be used - given that the CIP max for the 9x57 and 9x57R is 2800 bar, we are for sure on the safe side. CIP does not quote pressures for the 9,3x57 and x57R, I'm afraid. This also gave the 9,3mm a bad name, as the trajectory for sure is arcing!
V0 for the Sako load is given as 669m/s, i.e. 2195 fps.
I have not been able to track down actual load data, but I seem to recollect the last Lapua loads used an unnecessarily soft bullet. Sako's factory loads were the last ones but even this load was discontinued some years ago. It can still be found in the gun shops, though. This used the Gamehead bullet rather than the Hammerhead making it a tad too soft for moose.
For the handloader this is of course still a viable option, but otherwise it is in the words of Boddington "a dead duck".
We'll probably also see the demise of the 8,2mm soon. Sako no longer loads the 8g (127grs) FMJ bullet, and being owned by Beretta they're in the business of making money, not to keep obsolete calibers going. Which does not make it a bad choice either, as there are plenty of 8mm bullets on the market.
One of the problems with both of these are that they're so-called "semi-wildcats" or "factory wildcats", as they have only ever been known in Finland and loaded for this market by the domestic makers only. Thus, there is little load data but as said: the data from the similarish German calibers can be borrowed (without taking a standpoint to the viability NOR safety of this option, as I'm no handloader!).

About the guns in Finland:
There are plenty of rumors around these rifles, partly a confusion caused by the aforementioned misnomination of rifles in general.
According to the State Inventory of 1919, the total number of rifles run to 200 000 units. There were 3611 Winchester rifles - hardly the "majority" of the Russian contract rifles!
However, there are still rumors of a couple of train wagons full of 1895 Winchesters being delivered to Helsinki, the capital. I sure would like to get my hands on that consignment!!!
The total number of rifles supplied to the czar's army was close 300 000 units (according to the Winchester m/ 1895 manual). According to the mentioned article, 100 000 rifles were ordered in 1914, and 200 000 more in 1915 (the text is a bit vague, this later lot may have been ordered later). The shipment of these was canceled by Winchester before completion due to the revolution as payment was jeopardized. Some claim no rifles were paid for, but considering two lots being ordered, the first one for sure must have been paid for.
Some rifles have for sure later found their way to Finland, and the inventory did of course only include the rifles in the government's books. Given the population of Finland in 1917 being 3,2 million, there cannot have been many thousands of Winchester rifles lying around, I think. And at least not the majority of the weapons shipped!
Alas, I do not have any statistics as to the private ownership although those guns have always been well registered. Having said that, a couple of thousand of illegal weapons are turned in to the police annually, and the years after gaining independence and after WWII were turbulent, indeed. Thus, the number of illegal i.e. unregistered weapons especially in the countryside will for ever remain a mystery.
For comparison, today there are some 2 million registered firearms in Finland and the population is approx. 5,3 million.
However, I think these figures prove wrong the belief that the troops based in Finland were armed with the Winchesters - at least not exclusively. Of course some troops along the "border" (there was no real border as until independence Finland was an autonomous state of Russia) may have been so armed as "secondary" troops, but of this I have no proof. It would explain the belief of the rifles being supplied to the troops based in Finland. One could of course check the number of Russian troops in Finland at the time. I doubt the figure was many many thousands. You see, the garrisons then built could not have housed that many troops, and the garrisons are well kept or at least their locations are known, so if, say, 150 000 rifles would have been delivered here then the number of troops would have been quite exorbitant. So I simply cannot buy this.
The last rifles were take off the Finnish army's inventory in 1951 when there still were 41 Winchesters in the books - only 4 of these serviceable. Thus ended this chapter of the military use of the Winchester model 1895.

Finally:
Mr. 9,3x57, that's an impressive collection!!!

(Although photo "only"!!!!) Love it.

I really like the model 1895, and I'm having mine modified. I know: one should keep it original, but as the barrel's already been cut, the stock modified, the caliber not being original and the original sights together with the "ears" for the cartridge clip lost I think this is not a salvation project anymore.
I'll have the sights re-done once more, the stock re-done to fit me better (I shall store the old rear stock, as it's still original), and convert it to take-down.
Then it'll still see some more service. After all, it's only 90 years old. A rifle in it's best age, no?

- Lars/Finland